Properties

Label 12075m
Number of curves $1$
Conductor $12075$
CM no
Rank $1$

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

Elliptic curves in class 12075m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12075.b1 12075m1 \([0, -1, 1, -2408, -52282]\) \(-98867482624/20696067\) \(-323376046875\) \([]\) \(24000\) \(0.93024\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12075m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 12075m do not have complex multiplication.

Modular form 12075.2.a.m

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + q^{9} - 5 q^{11} - 2 q^{12} + 2 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display