Properties

Label 2075.d
Number of curves $1$
Conductor $2075$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2075.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2075.d1 2075a1 \([1, 0, 1, 24, -27]\) \(103823/83\) \(-1296875\) \([]\) \(256\) \(-0.13915\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2075.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 2075.d do not have complex multiplication.

Modular form 2075.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} + 3 q^{7} - 3 q^{8} - 2 q^{9} + 3 q^{11} - q^{12} + 6 q^{13} + 3 q^{14} - q^{16} - 5 q^{17} - 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display