# Properties

 Label 317900e Number of curves 4 Conductor 317900 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("317900.e1")

sage: E.isogeny_class()

## Elliptic curves in class 317900e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
317900.e4 317900e1 [0, 1, 0, -327533, 70560688] [2] 4478976 $$\Gamma_0(N)$$-optimal
317900.e3 317900e2 [0, 1, 0, -724908, -134484812] [2] 8957952
317900.e2 317900e3 [0, 1, 0, -3217533, -2194476812] [2] 13436928
317900.e1 317900e4 [0, 1, 0, -51299908, -141441034812] [2] 26873856

## Rank

sage: E.rank()

The elliptic curves in class 317900e have rank $$1$$.

## Modular form 317900.2.a.e

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.