Properties

Label 12075.m
Number of curves $1$
Conductor $12075$
CM no
Rank $0$

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

Elliptic curves in class 12075.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12075.m1 12075h1 \([0, -1, 1, 729217, -539549032]\) \(2744564518708084736/9629735831296875\) \(-150464622364013671875\) \([]\) \(224640\) \(2.5547\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12075.m1 has rank \(0\).

Complex multiplication

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

Modular form 12075.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} + q^{7} + q^{9} + q^{11} + 2 q^{12} + 4 q^{16} - 2 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display