Properties

Label 10051.d
Number of curves $1$
Conductor $10051$
CM no
Rank $0$

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

Elliptic curves in class 10051.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10051.d1 10051a1 \([0, -1, 1, 9875, -1299190]\) \(719323136/5316979\) \(-787103713059331\) \([]\) \(42240\) \(1.5398\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10051.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 10051.d do not have complex multiplication.

Modular form 10051.2.a.d

sage: E.q_eigenform(10)
 
\(q + 2q^{3} - 2q^{4} + q^{5} + 5q^{7} + q^{9} + q^{11} - 4q^{12} + 2q^{15} + 4q^{16} + 7q^{17} - q^{19} + O(q^{20})\)  Toggle raw display