Properties

Label 121275dm
Number of curves $1$
Conductor $121275$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("dm1")
 
E.isogeny_class()
 

Elliptic curves in class 121275dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121275.c1 121275dm1 \([0, 0, 1, -1392825, 634753656]\) \(-222985990144/841995\) \(-1128353828928046875\) \([]\) \(3096576\) \(2.3233\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121275dm1 has rank \(1\).

Complex multiplication

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

Modular form 121275.2.a.dm

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