Properties

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

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Show commands: SageMath
E = EllipticCurve("jf1")
 
E.isogeny_class()
 

Elliptic curves in class 78400jf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.a1 78400jf1 \([0, 0, 0, -2018800, 1137388000]\) \(-30211716096/1071875\) \(-32282885600000000000\) \([]\) \(4423680\) \(2.5157\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400jf1 has rank \(1\).

Complex multiplication

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

Modular form 78400.2.a.jf

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