Properties

Label 412224.a
Number of curves $1$
Conductor $412224$
CM no
Rank $2$

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

Elliptic curves in class 412224.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412224.a1 412224a1 \([0, -1, 0, -5505, 156801]\) \(140787677378/2325201\) \(304768745472\) \([]\) \(755712\) \(1.0023\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 412224.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 412224.a do not have complex multiplication.

Modular form 412224.2.a.a

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