# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2420.d1")

sage: E.isogeny_class()

## Elliptic curves in class 2420.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.d1 2420a2 [0, 0, 0, -177023, 28667078]  12672
2420.d2 2420a1 [0, 0, 0, -10648, 483153]  6336 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form2420.2.a.d

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 LMFDB 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 LMFDB labels. 