# Properties

 Label 1694.i Number of curves $2$ Conductor $1694$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1694.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1694.i1 1694i2 $$[1, 1, 1, -28377, 1828091]$$ $$1426487591593/2156$$ $$3819485516$$ $$$$ $$3840$$ $$1.1066$$
1694.i2 1694i1 $$[1, 1, 1, -1757, 28579]$$ $$-338608873/13552$$ $$-24008194672$$ $$$$ $$1920$$ $$0.76006$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1694.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1694.i do not have complex multiplication.

## Modular form1694.2.a.i

sage: E.q_eigenform(10)

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

## 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. 