Properties

Label 1694c
Number of curves $1$
Conductor $1694$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 1694c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1694.b1 1694c1 \([1, -1, 0, -50, -236]\) \(-115538049/153664\) \(-18593344\) \([]\) \(288\) \(0.087654\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1694c1 has rank \(1\).

Complex multiplication

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

Modular form 1694.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} - 3 q^{9} + q^{10} + q^{13} - q^{14} + q^{16} + q^{17} + 3 q^{18} + O(q^{20})\) Copy content Toggle raw display