# Properties

 Label 34650.ec Number of curves 4 Conductor 34650 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("34650.ec1")

sage: E.isogeny_class()

## Elliptic curves in class 34650.ec

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
34650.ec1 34650dp4 [1, -1, 1, -7422980, -7782276103] [2] 1179648
34650.ec2 34650dp2 [1, -1, 1, -477230, -114168103] [2, 2] 589824
34650.ec3 34650dp1 [1, -1, 1, -112730, 12677897] [2] 294912 $$\Gamma_0(N)$$-optimal
34650.ec4 34650dp3 [1, -1, 1, 636520, -568578103] [2] 1179648

## Rank

sage: E.rank()

The elliptic curves in class 34650.ec have rank $$1$$.

## Modular form 34650.2.a.ec

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} + q^{11} - 2q^{13} + q^{14} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.