# Properties

 Label 112710.ct Number of curves 2 Conductor 112710 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("112710.ct1")

sage: E.isogeny_class()

## Elliptic curves in class 112710.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
112710.ct1 112710ck1 [1, 0, 0, -3936186, 2971212516]  4423680 $$\Gamma_0(N)$$-optimal
112710.ct2 112710ck2 [1, 0, 0, -606906, 7837954020]  8847360

## Rank

sage: E.rank()

The elliptic curves in class 112710.ct have rank $$1$$.

## Modular form 112710.2.a.ct

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} + q^{12} - q^{13} + 2q^{14} - q^{15} + q^{16} + q^{18} + 2q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 