Properties

Label 382200.ip
Number of curves $1$
Conductor $382200$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("ip1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 382200.ip

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.ip1 382200ip1 \([0, 1, 0, 2037992, -102452512]\) \(10149078716/5923125\) \(-546330190770000000000\) \([]\) \(10838016\) \(2.6686\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 382200.ip1 has rank \(1\).

Complex multiplication

The elliptic curves in class 382200.ip do not have complex multiplication.

Modular form 382200.2.a.ip

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