Properties

Label 5194.c
Number of curves $1$
Conductor $5194$
CM no
Rank $1$

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

Elliptic curves in class 5194.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5194.c1 5194i1 \([1, 0, 1, -1349, 18960]\) \(-2305199161/1696\) \(-199532704\) \([]\) \(3600\) \(0.52670\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5194.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5194.c do not have complex multiplication.

Modular form 5194.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - q^{8} + q^{9} + q^{10} + 5 q^{11} - 2 q^{12} + 4 q^{13} + 2 q^{15} + q^{16} - 3 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display