# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("714.d1")

sage: E.isogeny_class()

## Elliptic curves in class 714a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
714.d2 714a1 [1, 1, 0, -3334, 81940] [2] 1344 $$\Gamma_0(N)$$-optimal
714.d1 714a2 [1, 1, 0, -55174, 4965268] [2] 2688

## Rank

sage: E.rank()

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

## Modular form714.2.a.d

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.