Properties

Label 214774c
Number of curves $1$
Conductor $214774$
CM no
Rank $1$

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

Elliptic curves in class 214774c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
214774.m1 214774c1 \([1, 1, 1, -53969, -4861137]\) \(-117433042273/363776\) \(-53851903556864\) \([]\) \(805376\) \(1.5028\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 214774c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 214774c do not have complex multiplication.

Modular form 214774.2.a.c

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