# Properties

 Label 254320.e Number of curves $4$ Conductor $254320$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 254320.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
254320.e1 254320e4 [0, 1, 0, -2051996, 1130707480] [2] 4478976
254320.e2 254320e3 [0, 1, 0, -128701, 17504334] [2] 2239488
254320.e3 254320e2 [0, 1, 0, -28996, 1064280] [2] 1492992
254320.e4 254320e1 [0, 1, 0, -13101, -569726] [2] 746496 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 254320.e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 254320.e do not have complex multiplication.

## Modular form 254320.2.a.e

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} - 4q^{7} + q^{9} - q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})$$

## 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.