Properties

Label 291312fi
Number of curves $1$
Conductor $291312$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fi1")
 
E.isogeny_class()
 

Elliptic curves in class 291312fi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
291312.fi1 291312fi1 \([0, 0, 0, -91722531, -346484244958]\) \(-1184052061112257/34349180544\) \(-2475696400714685414375424\) \([]\) \(46448640\) \(3.4599\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 291312fi1 has rank \(1\).

Complex multiplication

The elliptic curves in class 291312fi do not have complex multiplication.

Modular form 291312.2.a.fi

sage: E.q_eigenform(10)
 
\(q + 3 q^{5} - q^{7} - q^{11} + q^{13} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display