# Properties

 Label 51714.v Number of curves $4$ Conductor $51714$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 51714.v

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 51714.v do not have complex multiplication.

## 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 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. 