# Properties

 Label 95370.cd Number of curves 2 Conductor 95370 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("95370.cd1")

sage: E.isogeny_class()

## Elliptic curves in class 95370.cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95370.cd1 95370cf2 [1, 1, 1, -3398646, 2408803443]  3096576
95370.cd2 95370cf1 [1, 1, 1, -254326, 21635699]  1548288 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 95370.cd have rank $$1$$.

## Modular form 95370.2.a.cd

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} + q^{11} - q^{12} - 4q^{13} + 2q^{14} + q^{15} + q^{16} + q^{18} - 6q^{19} + O(q^{20})$$

## 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. 