Properties

Label 25857m
Number of curves $1$
Conductor $25857$
CM no
Rank $0$

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25857m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25857.s1 25857m1 \([0, 0, 1, -85683, 17172301]\) \(-692224/867\) \(-87132494763717507\) \([]\) \(544128\) \(1.9439\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 25857m1 has rank \(0\).

Complex multiplication

The elliptic curves in class 25857m do not have complex multiplication.

Modular form 25857.2.a.m

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