# Properties

 Label 25270c Number of curves $4$ Conductor $25270$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("25270.e1")

sage: E.isogeny_class()

## Elliptic curves in class 25270c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25270.e4 25270c1 [1, -1, 0, 835, 14581] [2] 28800 $$\Gamma_0(N)$$-optimal
25270.e3 25270c2 [1, -1, 0, -6385, 160425] [2, 2] 57600
25270.e2 25270c3 [1, -1, 0, -31655, -2017849] [2] 115200
25270.e1 25270c4 [1, -1, 0, -96635, 11586075] [2] 115200

## Rank

sage: E.rank()

The elliptic curves in class 25270c have rank $$0$$.

## Modular form 25270.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} - 3q^{9} + q^{10} + 4q^{11} + 6q^{13} + q^{14} + q^{16} + 2q^{17} + 3q^{18} + O(q^{20})$$

## 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 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.