Properties

Label 67270.c
Number of curves $1$
Conductor $67270$
CM no
Rank $1$

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

Elliptic curves in class 67270.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67270.c1 67270o1 \([1, -1, 0, -119344, -15728672]\) \(211815318681/1701280\) \(1509892262411680\) \([]\) \(691200\) \(1.7399\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67270.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 67270.c do not have complex multiplication.

Modular form 67270.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} + q^{4} + q^{5} + 3 q^{6} - q^{7} - q^{8} + 6 q^{9} - q^{10} + q^{11} - 3 q^{12} + q^{13} + q^{14} - 3 q^{15} + q^{16} - 6 q^{17} - 6 q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display