Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 30345.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30345.r1 30345bc1 \([0, 1, 1, -1375597035, 19640181457964]\) \(-11926249134908509075308544/2246680441062421875\) \(-54229404167094641314921875\) \([]\) \(12096000\) \(3.9395\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 30345.r1 has rank \(1\).

Complex multiplication

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

Modular form 30345.2.a.r

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