Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 121275.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121275.u1 121275et1 \([0, 0, 1, -3675, 9464656]\) \(-4096/28875\) \(-38695261623046875\) \([]\) \(1327104\) \(1.8618\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121275.u1 has rank \(2\).

Complex multiplication

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

Modular form 121275.2.a.u

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