Properties

Label 1215.c
Number of curves $1$
Conductor $1215$
CM no
Rank $1$

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

Elliptic curves in class 1215.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1215.c1 1215i1 \([1, -1, 1, -2, 4]\) \(-2187/25\) \(-6075\) \([]\) \(72\) \(-0.59206\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1215.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1215.c do not have complex multiplication.

Modular form 1215.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + 3 q^{7} + 3 q^{8} - q^{10} - 4 q^{11} - 5 q^{13} - 3 q^{14} - q^{16} - 4 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display