# Properties

 Label 690.i Number of curves $2$ Conductor $690$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 690.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
690.i1 690i2 $$[1, 0, 0, -786, -5940]$$ $$53706380371489/16171875000$$ $$16171875000$$ $$$$ $$480$$ $$0.66410$$
690.i2 690i1 $$[1, 0, 0, 134, -604]$$ $$265971760991/317400000$$ $$-317400000$$ $$$$ $$240$$ $$0.31753$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 690.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 690.i do not have complex multiplication.

## Modular form690.2.a.i

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 