# Properties

 Label 2420.f Number of curves 2 Conductor 2420 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2420.f1")

sage: E.isogeny_class()

## Elliptic curves in class 2420.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.f1 2420c2 [0, 1, 0, -436, 3364] [] 432
2420.f2 2420c1 [0, 1, 0, 4, 20] [] 144 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2420.f have rank $$1$$.

## Modular form2420.2.a.f

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{7} - 2q^{9} - 2q^{13} - q^{15} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.