# Properties

 Label 2420.a Number of curves 4 Conductor 2420 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2420.a1")

sage: E.isogeny_class()

## Elliptic curves in class 2420.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.a1 2420e3 [0, 1, 0, -5001, 134440]  2160
2420.a2 2420e4 [0, 1, 0, -4396, 168804]  4320
2420.a3 2420e1 [0, 1, 0, -161, -596]  720 $$\Gamma_0(N)$$-optimal
2420.a4 2420e2 [0, 1, 0, 444, -3500]  1440

## Rank

sage: E.rank()

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

## Modular form2420.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} - 2q^{7} + q^{9} - 2q^{13} + 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 