Properties

Label 3450.e
Number of curves $1$
Conductor $3450$
CM no
Rank $1$

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

Elliptic curves in class 3450.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.e1 3450g1 \([1, 1, 0, -3450, 76500]\) \(11631015625/13248\) \(5175000000\) \([]\) \(2880\) \(0.77723\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3450.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3450.e do not have complex multiplication.

Modular form 3450.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 5q^{11} - q^{12} + 3q^{13} - q^{14} + q^{16} + 2q^{17} - q^{18} - 3q^{19} + O(q^{20})\)  Toggle raw display