Properties

 Label 51714s Number of curves 4 Conductor 51714 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("51714.v1")

sage: E.isogeny_class()

Elliptic curves in class 51714s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
51714.v4 51714s1 [1, -1, 1, -4595, -73069] [2] 110592 $$\Gamma_0(N)$$-optimal
51714.v3 51714s2 [1, -1, 1, -65435, -6424765] [2] 221184
51714.v2 51714s3 [1, -1, 1, -156695, 23910059] [2] 331776
51714.v1 51714s4 [1, -1, 1, -171905, 19000271] [2] 663552

Rank

sage: E.rank()

The elliptic curves in class 51714s have rank $$0$$.

Modular form 51714.2.a.v

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 4q^{7} + q^{8} + 6q^{11} + 4q^{14} + q^{16} + q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.