Properties

Label 68970.k
Number of curves $1$
Conductor $68970$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 68970.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68970.k1 68970q1 \([1, 1, 0, 7582463, 81276661]\) \(3292939724890125839639/1905816470814720000\) \(-27903058949198315520000\) \([]\) \(7257600\) \(2.9964\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 68970.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 68970.k do not have complex multiplication.

Modular form 68970.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 3 q^{7} - q^{8} + q^{9} - q^{10} - q^{12} + 3 q^{13} + 3 q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display