Properties

Label 121968r
Number of curves $1$
Conductor $121968$
CM no
Rank $1$

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

Elliptic curves in class 121968r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121968.cr1 121968r1 \([0, 0, 0, -363, -11979]\) \(-6912/77\) \(-58929205104\) \([]\) \(61440\) \(0.74864\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121968r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 121968r do not have complex multiplication.

Modular form 121968.2.a.r

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