# Properties

 Label 95304v Number of curves 4 Conductor 95304 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("95304.x1")

sage: E.isogeny_class()

## Elliptic curves in class 95304v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95304.x3 95304v1 [0, 1, 0, -4452, 108768]  115200 $$\Gamma_0(N)$$-optimal
95304.x2 95304v2 [0, 1, 0, -11672, -341760] [2, 2] 230400
95304.x4 95304v3 [0, 1, 0, 31648, -2247840]  460800
95304.x1 95304v4 [0, 1, 0, -170512, -27153952]  460800

## Rank

sage: E.rank()

The elliptic curves in class 95304v have rank $$1$$.

## Modular form 95304.2.a.x

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{9} + q^{11} - 2q^{13} + 2q^{15} + 6q^{17} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 