Properties

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

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Show commands: SageMath
E = EllipticCurve("fj1")
 
E.isogeny_class()
 

Elliptic curves in class 78400fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.jb1 78400fj1 \([0, -1, 0, -80033, 4757537]\) \(2450\) \(23140372398080000\) \([]\) \(548352\) \(1.8377\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400fj1 has rank \(1\).

Complex multiplication

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

Modular form 78400.2.a.fj

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{9} - 4 q^{11} - 2 q^{13} + 3 q^{17} + O(q^{20})\) Copy content Toggle raw display