Properties

Label 258c
Number of curves $1$
Conductor $258$
CM no
Rank $1$

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

Elliptic curves in class 258c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
258.c1 258c1 \([1, 0, 1, -15, 22]\) \(-338608873/41796\) \(-41796\) \([]\) \(40\) \(-0.37868\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 258c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 258c do not have complex multiplication.

Modular form 258.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - 3 q^{7} - q^{8} + q^{9} + 3 q^{10} - 5 q^{11} + q^{12} - 3 q^{13} + 3 q^{14} - 3 q^{15} + q^{16} - q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display