Properties

Label 2031.c
Number of curves $1$
Conductor $2031$
CM no
Rank $1$

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

Elliptic curves in class 2031.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2031.c1 2031b1 \([0, -1, 1, -201848, 29995379]\) \(909492695602190848000/139388296428077373\) \(139388296428077373\) \([]\) \(24960\) \(2.0133\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2031.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2031.c do not have complex multiplication.

Modular form 2031.2.a.c

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{7} + q^{9} - 2 q^{12} + 3 q^{13} - 4 q^{14} - 4 q^{16} - 6 q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display