Properties

Label 78400gc
Number of curves $1$
Conductor $78400$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("gc1")
 
E.isogeny_class()
 

Elliptic curves in class 78400gc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.dy1 78400gc1 \([0, -1, 0, -1633, 171137]\) \(-196/5\) \(-12293120000000\) \([]\) \(110592\) \(1.1923\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400gc1 has rank \(2\).

Complex multiplication

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

Modular form 78400.2.a.gc

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