Properties

Label 714c
Number of curves $1$
Conductor $714$
CM no
Rank $0$

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

Elliptic curves in class 714c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
714.c1 714c1 \([1, 1, 0, -14597, -686643]\) \(-344002044213921241/1011143540736\) \(-1011143540736\) \([]\) \(2040\) \(1.1738\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 714c1 has rank \(0\).

Complex multiplication

The elliptic curves in class 714c do not have complex multiplication.

Modular form 714.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + 5 q^{11} - q^{12} - q^{13} - q^{14} - q^{15} + q^{16} - q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display