Properties

Label 1001.c
Number of curves $1$
Conductor $1001$
CM no
Rank $1$

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

Elliptic curves in class 1001.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1001.c1 1001a1 \([0, -1, 1, -15881, 778423]\) \(-442980486619070464/1864582578859\) \(-1864582578859\) \([]\) \(1680\) \(1.2092\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1001.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1001.c do not have complex multiplication.

Modular form 1001.2.a.c

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{4} - q^{5} - q^{7} + q^{9} - q^{11} - 4 q^{12} - q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display