Properties

Label 1216.f
Number of curves $1$
Conductor $1216$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1216.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1216.f1 1216c1 \([0, -1, 0, -33, -95]\) \(-31250/19\) \(-2490368\) \([]\) \(128\) \(-0.070605\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1216.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1216.f do not have complex multiplication.

Modular form 1216.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3q^{7} - 2q^{9} - 2q^{11} - q^{13} - 5q^{17} - q^{19} + O(q^{20})\)  Toggle raw display