Properties

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

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 78400.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.ed1 78400hw1 \([0, -1, 0, 1051867, 1301880637]\) \(12459008/78125\) \(-807072140000000000000\) \([]\) \(2408448\) \(2.6935\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400.ed1 has rank \(1\).

Complex multiplication

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

Modular form 78400.2.a.ed

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{9} + 3 q^{11} - q^{13} - 5 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display