Properties

Label 68970p
Number of curves $1$
Conductor $68970$
CM no
Rank $1$

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

Elliptic curves in class 68970p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68970.i1 68970p1 \([1, 1, 0, -28007872, 57237247456]\) \(-11335027914992789161/45438205500000\) \(-9740082885628045500000\) \([]\) \(8870400\) \(3.0760\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 68970p1 has rank \(1\).

Complex multiplication

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

Modular form 68970.2.a.p

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