Properties

Label 78400jc
Number of curves $1$
Conductor $78400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("jc1")
 
E.isogeny_class()
 

Elliptic curves in class 78400jc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.q1 78400jc1 \([0, 0, 0, 980, -27440]\) \(270\) \(-385512243200\) \([]\) \(138240\) \(0.90601\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400jc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 78400jc do not have complex multiplication.

Modular form 78400.2.a.jc

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