Properties

Label 1012.d
Number of curves $1$
Conductor $1012$
CM no
Rank $0$

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

Elliptic curves in class 1012.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1012.d1 1012a1 \([0, 1, 0, -884166, 319707497]\) \(-4777554520541237119744/49850049369527\) \(-797600789912432\) \([]\) \(13776\) \(2.0164\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1012.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1012.d do not have complex multiplication.

Modular form 1012.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9} - q^{11} + 3 q^{13} + 4 q^{15} + 6 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display