Properties

Label 6958.a
Number of curves $1$
Conductor $6958$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 6958.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6958.a1 6958i1 \([1, -1, 0, -128683, -17662331]\) \(2003092024307193/9529458688\) \(1121131285184512\) \([]\) \(106920\) \(1.7370\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6958.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6958.a do not have complex multiplication.

Modular form 6958.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + 3 q^{6} - q^{8} + 6 q^{9} + 2 q^{10} - 6 q^{11} - 3 q^{12} + 5 q^{13} + 6 q^{15} + q^{16} - 6 q^{17} - 6 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display