Properties

Label 30345.b
Number of curves $1$
Conductor $30345$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 30345.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30345.b1 30345z1 \([0, 1, 1, -266, 1580]\) \(7229403136/19845\) \(5735205\) \([]\) \(12672\) \(0.17002\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 30345.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 30345.b do not have complex multiplication.

Modular form 30345.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - 2 q^{6} + q^{7} + q^{9} + 2 q^{10} + 3 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - q^{15} - 4 q^{16} - 2 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display