Properties

Label 2415c
Number of curves $1$
Conductor $2415$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 2415c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2415.f1 2415c1 \([0, 1, 1, 29169, -4304725]\) \(2744564518708084736/9629735831296875\) \(-9629735831296875\) \([]\) \(9360\) \(1.7499\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2415c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2415c do not have complex multiplication.

Modular form 2415.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - q^{5} - q^{7} + q^{9} + q^{11} - 2 q^{12} - q^{15} + 4 q^{16} + 2 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display