Properties

Label 32192bd
Number of curves $1$
Conductor $32192$
CM no
Rank $1$

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

Elliptic curves in class 32192bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32192.c1 32192bd1 \([0, 0, 0, 1436, 27712]\) \(79951586112/127263527\) \(-521271406592\) \([]\) \(57600\) \(0.93348\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32192bd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 32192bd do not have complex multiplication.

Modular form 32192.2.a.bd

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