Properties

Label 323400.ei
Number of curves $1$
Conductor $323400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ei1")
 
E.isogeny_class()
 

Elliptic curves in class 323400.ei

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
323400.ei1 323400ei1 \([0, -1, 0, -1248775208, -17240316213588]\) \(-91528907990864450/1604769890031\) \(-3775991455845142380000000000\) \([]\) \(191600640\) \(4.0889\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 323400.ei1 has rank \(1\).

Complex multiplication

The elliptic curves in class 323400.ei do not have complex multiplication.

Modular form 323400.2.a.ei

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + q^{11} + 4 q^{13} - 4 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display