Properties

Label 608a
Number of curves $1$
Conductor $608$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 608a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
608.c1 608a1 \([0, 0, 0, -8, -16]\) \(-13824/19\) \(-77824\) \([]\) \(32\) \(-0.36899\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 608a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 608a do not have complex multiplication.

Modular form 608.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 3 q^{9} - 3 q^{11} - 4 q^{13} - 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display