Properties

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

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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 \([1, 1, 1, -28377, 1828091]\) \(1426487591593/2156\) \(3819485516\) \([2]\) \(3840\) \(1.1066\)  
1694.i2 1694i1 \([1, 1, 1, -1757, 28579]\) \(-338608873/13552\) \(-24008194672\) \([2]\) \(1920\) \(0.76006\) \(\Gamma_0(N)\)-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 form 1694.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + q^{8} + q^{9} + 2 q^{10} + 2 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.