Properties

Label 100005.c
Number of curves $1$
Conductor $100005$
CM no
Rank $1$

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

Elliptic curves in class 100005.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100005.c1 100005d1 \([1, 0, 1, -1133, -77407]\) \(-160643187047881/2489186953125\) \(-2489186953125\) \([]\) \(180096\) \(1.0599\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100005.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100005.c do not have complex multiplication.

Modular form 100005.2.a.c

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