# Properties

 Label 79420.e Number of curves 4 Conductor 79420 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("79420.e1")

sage: E.isogeny_class()

## Elliptic curves in class 79420.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
79420.e1 79420b4 [0, -1, 0, -2563220, 1580381000]  1492992
79420.e2 79420b3 [0, -1, 0, -160765, 24551142]  746496
79420.e3 79420b2 [0, -1, 0, -36220, 1511400]  497664
79420.e4 79420b1 [0, -1, 0, -16365, -783838]  248832 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 79420.e have rank $$0$$.

## Modular form 79420.2.a.e

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} - 4q^{7} + q^{9} - q^{11} + 4q^{13} + 2q^{15} + O(q^{20})$$

## 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. 