Properties

Label 378.a
Number of curves $1$
Conductor $378$
CM no
Rank $0$

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

Elliptic curves in class 378.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
378.a1 378h1 \([1, -1, 0, 441, -1571]\) \(38983348653/26353376\) \(-6403870368\) \([]\) \(420\) \(0.57037\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 378.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 378.a do not have complex multiplication.

Modular form 378.2.a.a

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