# Properties

 Label 714.i Number of curves $3$ Conductor $714$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("714.i1")

sage: E.isogeny_class()

## Elliptic curves in class 714.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
714.i1 714i3 [1, 0, 0, -381702, -90803346] [] 9720
714.i2 714i2 [1, 0, 0, -972, -315144]  3240
714.i3 714i1 [1, 0, 0, 108, 11664]  1080 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 714.i have rank $$0$$.

## Modular form714.2.a.i

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - 3q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - 3q^{10} + 3q^{11} + q^{12} + 5q^{13} + q^{14} - 3q^{15} + q^{16} - q^{17} + q^{18} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 