Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 3450.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.w1 3450t1 \([1, 0, 0, -138, 612]\) \(11631015625/13248\) \(331200\) \([]\) \(576\) \(-0.027487\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3450.w1 has rank \(1\).

Complex multiplication

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

Modular form 3450.2.a.w

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