Properties

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

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Show commands: SageMath
E = EllipticCurve("hg1")
 
E.isogeny_class()
 

Elliptic curves in class 78400hg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.if1 78400hg1 \([0, 1, 0, -80033, -58539937]\) \(-196/5\) \(-1446273274880000000\) \([]\) \(774144\) \(2.1652\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400hg1 has rank \(1\).

Complex multiplication

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

Modular form 78400.2.a.hg

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{9} + 2 q^{11} + 4 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display