Properties

Label 2072.d
Number of curves $1$
Conductor $2072$
CM no
Rank $1$

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

Elliptic curves in class 2072.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2072.d1 2072b1 \([0, 0, 0, 4, -12]\) \(27648/259\) \(-66304\) \([]\) \(192\) \(-0.39362\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2072.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2072.d do not have complex multiplication.

Modular form 2072.2.a.d

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