Properties

Label 27448.a
Number of curves $1$
Conductor $27448$
CM no
Rank $3$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 27448.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27448.a1 27448d1 \([0, 0, 0, -79, 274]\) \(-212992848/3431\) \(-878336\) \([]\) \(14080\) \(-0.058945\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 27448.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 27448.a do not have complex multiplication.

Modular form 27448.2.a.a

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