Properties

Label 1848.a
Number of curves $1$
Conductor $1848$
CM no
Rank $1$

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

Elliptic curves in class 1848.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1848.a1 1848c1 \([0, -1, 0, -12, 21]\) \(-12967168/231\) \(-3696\) \([]\) \(160\) \(-0.51861\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1848.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1848.a do not have complex multiplication.

Modular form 1848.2.a.a

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