# Properties

 Label 2420b Number of curves 2 Conductor 2420 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2420.c1")

sage: E.isogeny_class()

## Elliptic curves in class 2420b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.c2 2420b1 [0, 0, 0, -88, -363]  576 $$\Gamma_0(N)$$-optimal
2420.c1 2420b2 [0, 0, 0, -1463, -21538]  1152

## Rank

sage: E.rank()

The elliptic curves in class 2420b have rank $$0$$.

## Modular form2420.2.a.c

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} - 3q^{9} - 4q^{13} + 4q^{17} - 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 