# Properties

 Label 95304.d Number of curves 4 Conductor 95304 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("95304.d1")

sage: E.isogeny_class()

## Elliptic curves in class 95304.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95304.d1 95304n4 [0, -1, 0, -254264, -49263972] [2] 580608
95304.d2 95304n3 [0, -1, 0, -37664, 1749660] [2] 580608
95304.d3 95304n2 [0, -1, 0, -16004, -754236] [2, 2] 290304
95304.d4 95304n1 [0, -1, 0, 241, -39456] [2] 145152 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 95304.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} + 4q^{7} + q^{9} - q^{11} - 6q^{13} + 2q^{15} + 6q^{17} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.