Properties

Label 303450.ei
Number of curves $1$
Conductor $303450$
CM no
Rank $1$

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

Elliptic curves in class 303450.ei

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.ei1 303450ei1 \([1, 1, 1, -2149588, 2074904981]\) \(-72814163751025/81252605952\) \(-1225775239122631680000\) \([]\) \(14376960\) \(2.7410\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 303450.ei1 has rank \(1\).

Complex multiplication

The elliptic curves in class 303450.ei do not have complex multiplication.

Modular form 303450.2.a.ei

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} + 2 q^{11} - q^{12} - 2 q^{13} - q^{14} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display