Properties

Label 67158.p
Number of curves $1$
Conductor $67158$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 67158.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67158.p1 67158e1 \([1, -1, 0, -21939, -1245259]\) \(59332690053027/1671488\) \(32899898304\) \([]\) \(124416\) \(1.1201\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67158.p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 67158.p do not have complex multiplication.

Modular form 67158.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + 3 q^{11} + q^{13} + q^{14} + q^{16} + 5 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display