Properties

Label 74382.bd
Number of curves $1$
Conductor $74382$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 74382.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74382.bd1 74382bh1 \([1, 1, 1, -5685, -1635621]\) \(-172715635009/9694992384\) \(-1140606158985216\) \([]\) \(337920\) \(1.5691\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 74382.bd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 74382.bd do not have complex multiplication.

Modular form 74382.2.a.bd

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