Properties

Label 78400.z
Number of curves $1$
Conductor $78400$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 78400.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.z1 78400dl1 \([0, 0, 0, 156800, -72716000]\) \(14155776/84035\) \(-2530978231040000000\) \([]\) \(2211840\) \(2.2132\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400.z1 has rank \(0\).

Complex multiplication

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

Modular form 78400.2.a.z

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