Properties

Label 69300.e
Number of curves $1$
Conductor $69300$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 69300.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69300.e1 69300o1 \([0, 0, 0, -4604973000, -120278722387500]\) \(-799965408846201776676864/128959272851717\) \(-1740950183498179500000000\) \([]\) \(31749120\) \(4.0536\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 69300.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 69300.e do not have complex multiplication.

Modular form 69300.2.a.e

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