Properties

Label 76440r
Number of curves $1$
Conductor $76440$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 76440r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76440.s1 76440r1 \([0, -1, 0, 476215, -83396403]\) \(396555344454656/328867205355\) \(-9904869847759461120\) \([]\) \(1995840\) \(2.3327\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 76440r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 76440r do not have complex multiplication.

Modular form 76440.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 5 q^{11} - q^{13} - q^{15} - 3 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display