# Properties

 Label 2420f Number of curves 2 Conductor 2420 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2420.g1")

sage: E.isogeny_class()

## Elliptic curves in class 2420f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.g2 2420f1 [0, -1, 0, -645, -130] [2] 1440 $$\Gamma_0(N)$$-optimal
2420.g1 2420f2 [0, -1, 0, -7300, -237048] [2] 2880

## Rank

sage: E.rank()

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

## Modular form2420.2.a.g

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} + q^{9} + 2q^{15} + 4q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.