Gromov–Witten conjecture for elliptic Noether–Lefschetz loci

Let $\overline{\mathcal M}_{g,1}(\pi,d)$ be the moduli space of log-stable maps of degree $d$ to the fibers of the universal family of elliptic curves, with evaluation map $\mathsf{ev}$ and cotangent-line class $\psi$. For $\Lambda\in\mathsf{R}^*(\overline{\mathcal M}_g)$ divisible by $\lambda_g$, write $\langle\tau_i(s)\Lambda\rangle_{g,d}^\pi$ for the corresponding Gromov–Witten invariant. Gromov–Witten conjecture for elliptic Noether–Lefschetz loci. For all $g\geq 2$, $d\geq 1$, and such $\Lambda$,

$$\langle \tau_i(s)\Lambda \rangle_{g,d}^\pi:= \frac{g\sigma_{2g-1}(d)}{6|B_{2g}|}\int_{\overline{\mathcal M}_{g,1}}\psi^i\lambda_{g-1}\Lambda,$$

where $B_i$ is the $i$-th Bernoulli number and $\sigma_k(n)=\sum_{m\mid n}m^k$. This conjecture relates Gromov–Witten invariants of elliptic curves to tautological intersection numbers and divisor sums; the source presents it after identifying the relevant Noether–Lefschetz virtual class, and gives no resolution.