Properties

Label 32340.m
Number of curves $1$
Conductor $32340$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 32340.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.m1 32340g1 \([0, -1, 0, -698805, -224472303]\) \(61398847532302336/44027317125\) \(27061654634784000\) \([]\) \(362880\) \(2.0883\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32340.m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 32340.m do not have complex multiplication.

Modular form 32340.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - q^{11} + q^{13} - q^{15} - 4 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display