Properties

Label 1075.d
Number of curves $1$
Conductor $1075$
CM no
Rank $0$

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

Elliptic curves in class 1075.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1075.d1 1075a1 \([0, 0, 1, -200, -1469]\) \(-56623104/26875\) \(-419921875\) \([]\) \(192\) \(0.36051\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1075.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1075.d do not have complex multiplication.

Modular form 1075.2.a.d

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