Properties

Label 25857.a
Number of curves $1$
Conductor $25857$
CM no
Rank $2$

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25857.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25857.a1 25857p1 \([0, 0, 1, -507, 7816]\) \(-692224/867\) \(-18051780123\) \([]\) \(41856\) \(0.66141\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 25857.a1 has rank \(2\).

Complex multiplication

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

Modular form 25857.2.a.a

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