# Properties

 Label 54760c Number of curves 4 Conductor 54760 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54760.e1")

sage: E.isogeny_class()

## Elliptic curves in class 54760c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54760.e3 54760c1 [0, 0, 0, -2738, 50653] [2] 50688 $$\Gamma_0(N)$$-optimal
54760.e2 54760c2 [0, 0, 0, -9583, -303918] [2, 2] 101376
54760.e4 54760c3 [0, 0, 0, 17797, -1722202] [2] 202752
54760.e1 54760c4 [0, 0, 0, -146483, -21578178] [2] 202752

## Rank

sage: E.rank()

The elliptic curves in class 54760c have rank $$0$$.

## Modular form 54760.2.a.e

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} - 3q^{9} + 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 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.