# Properties

 Label 262080.m Number of curves 4 Conductor 262080 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("262080.m1")

sage: E.isogeny_class()

## Elliptic curves in class 262080.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.m1 262080m3 [0, 0, 0, -31008108, 66451951568]  23592960
262080.m2 262080m4 [0, 0, 0, -12643788, -16645282288]  23592960
262080.m3 262080m2 [0, 0, 0, -2113788, 838729712] [2, 2] 11796480
262080.m4 262080m1 [0, 0, 0, 350232, 86710808]  5898240 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 262080.m have rank $$0$$.

## Modular form 262080.2.a.m

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 4q^{11} + q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 