# Properties

 Label 57800s Number of curves 4 Conductor 57800 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("57800.n1")

sage: E.isogeny_class()

## Elliptic curves in class 57800s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
57800.n3 57800s1 [0, 0, 0, -14450, 614125]  122880 $$\Gamma_0(N)$$-optimal
57800.n2 57800s2 [0, 0, 0, -50575, -3684750] [2, 2] 245760
57800.n4 57800s3 [0, 0, 0, 93925, -20880250]  491520
57800.n1 57800s4 [0, 0, 0, -773075, -261617250]  491520

## Rank

sage: E.rank()

The elliptic curves in class 57800s have rank $$0$$.

## Modular form 57800.2.a.n

sage: E.q_eigenform(10)

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

## 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. 