Properties

Label 303450cm
Number of curves $1$
Conductor $303450$
CM no
Rank $2$

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Show commands for: SageMath
sage: E = EllipticCurve("cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.cm1 303450cm1 \([1, 0, 1, -3126, -40952]\) \(18694465225/6858432\) \(1238804280000\) \([]\) \(798336\) \(1.0207\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 303450cm1 has rank \(2\).

Complex multiplication

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

Modular form 303450.2.a.cm

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