Properties

Label 300069c
Number of curves $1$
Conductor $300069$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 300069c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
300069.c1 300069c1 \([0, 0, 1, -6051, -205664]\) \(-33610706587648/5614591059\) \(-4093036882011\) \([]\) \(795648\) \(1.1470\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 300069c1 has rank \(2\).

Complex multiplication

The elliptic curves in class 300069c do not have complex multiplication.

Modular form 300069.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - 2 q^{5} + q^{7} + 4 q^{10} + q^{11} + 3 q^{13} - 2 q^{14} - 4 q^{16} - 6 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display