# Properties

 Label 714.a Number of curves $2$ Conductor $714$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("714.a1")

sage: E.isogeny_class()

## Elliptic curves in class 714.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
714.a1 714d2 [1, 1, 0, -381, 2709] [2] 192
714.a2 714d1 [1, 1, 0, -21, 45] [2] 96 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 714.a have rank $$1$$.

## Modular form714.2.a.a

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.