Properties

Label 179776z
Number of curves $1$
Conductor $179776$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 179776z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
179776.m1 179776z1 \([0, -1, 0, -48689, 7868113]\) \(-35152/53\) \(-19246467315089408\) \([]\) \(1078272\) \(1.8163\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 179776z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 179776z do not have complex multiplication.

Modular form 179776.2.a.z

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