Properties

Label 4275m
Number of curves 11
Conductor 42754275
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 4275m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4275.c1 4275m1 [1,1,1,140,672][1, -1, 1, -140, 672] 16539745/57-16539745/57 1038825-1038825 [][] 768768 0.0178350.017835 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4275m1 has rank 11.

Complex multiplication

The elliptic curves in class 4275m do not have complex multiplication.

Modular form 4275.2.a.m

sage: E.q_eigenform(10)
 
qq2q44q7+3q83q11+4q14q16+q19+O(q20)q - q^{2} - q^{4} - 4 q^{7} + 3 q^{8} - 3 q^{11} + 4 q^{14} - q^{16} + q^{19} + O(q^{20}) Copy content Toggle raw display