Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 78400i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.ja1 78400i1 \([0, -1, 0, -40833, -1710463]\) \(2450\) \(3073280000000000\) \([]\) \(391680\) \(1.6694\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400i1 has rank \(1\).

Complex multiplication

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

Modular form 78400.2.a.i

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