Properties

Label 67270.h
Number of curves $1$
Conductor $67270$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 67270.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67270.h1 67270b1 \([1, 1, 0, -128, -128]\) \(7880599/4480\) \(133463680\) \([]\) \(25088\) \(0.24898\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67270.h1 has rank \(2\).

Complex multiplication

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

Modular form 67270.2.a.h

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