# Properties

 Label 325.a Number of curves 2 Conductor 325 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("325.a1")
sage: E.isogeny_class()

## Elliptic curves in class 325.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
325.a1 325e2 [0, -1, 1, -12708, -547182] 1 420
325.a2 325e1 [0, -1, 1, -98, 378] 5 84 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 325.a have rank $$0$$.

## Modular form325.2.a.a

sage: E.q_eigenform(10)
$$q - 2q^{2} - q^{3} + 2q^{4} + 2q^{6} - 2q^{7} - 2q^{9} + 2q^{11} - 2q^{12} + q^{13} + 4q^{14} - 4q^{16} - 2q^{17} + 4q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.