Properties

Label 34969m
Number of curves $1$
Conductor $34969$
CM no
Rank $1$

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

Elliptic curves in class 34969m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34969.a1 34969m1 \([0, 0, 1, -10106041, -12367267674]\) \(-9236754432/1331\) \(-16448471150982018731\) \([]\) \(3855600\) \(2.7025\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 34969m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 34969m do not have complex multiplication.

Modular form 34969.2.a.m

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 2 q^{5} + 6 q^{6} + 2 q^{7} + 6 q^{9} + 4 q^{10} - 6 q^{12} + 2 q^{13} - 4 q^{14} + 6 q^{15} - 4 q^{16} - 12 q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display