Properties

Label 605.c
Number of curves $1$
Conductor $605$
CM no
Rank $1$

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

Elliptic curves in class 605.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
605.c1 605a1 \([1, -1, 0, -1414, -44027]\) \(-1459161/3125\) \(-669871503125\) \([]\) \(1320\) \(0.95811\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 605.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 605.c do not have complex multiplication.

Modular form 605.2.a.c

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