Properties

Label 1305.c
Number of curves $1$
Conductor $1305$
CM no
Rank $1$

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

Elliptic curves in class 1305.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1305.c1 1305e1 \([0, 0, 1, 708, 29605]\) \(53838872576/550546875\) \(-401348671875\) \([]\) \(1120\) \(0.90760\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1305.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1305.c do not have complex multiplication.

Modular form 1305.2.a.c

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