Properties

Label 121275.p
Number of curves $1$
Conductor $121275$
CM no
Rank $2$

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

Elliptic curves in class 121275.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121275.p1 121275ev1 \([0, 0, 1, 2625, 187906]\) \(3584000/29403\) \(-16411008796875\) \([]\) \(414720\) \(1.2171\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121275.p1 has rank \(2\).

Complex multiplication

The elliptic curves in class 121275.p do not have complex multiplication.

Modular form 121275.2.a.p

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