# Properties

 Label 331200jf Number of curves $6$ Conductor $331200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("331200.jf1")

sage: E.isogeny_class()

## Elliptic curves in class 331200jf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
331200.jf5 331200jf1 [0, 0, 0, -6048300, -6281282000] [2] 14155776 $$\Gamma_0(N)$$-optimal
331200.jf4 331200jf2 [0, 0, 0, -99360300, -381208898000] [2, 2] 28311552
331200.jf3 331200jf3 [0, 0, 0, -101952300, -360270722000] [2, 2] 56623104
331200.jf1 331200jf4 [0, 0, 0, -1589760300, -24397514498000] [2] 56623104
331200.jf2 331200jf5 [0, 0, 0, -371952300, 2365109278000] [2] 113246208
331200.jf6 331200jf6 [0, 0, 0, 126575700, -1745607458000] [2] 113246208

## Rank

sage: E.rank()

The elliptic curves in class 331200jf have rank $$0$$.

## Modular form 331200.2.a.jf

sage: E.q_eigenform(10)

$$q + 4q^{11} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.