Properties

Label 464968.b
Number of curves $2$
Conductor $464968$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 464968.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
464968.b1 464968b2 \([0, 1, 0, -176288, -28545968]\) \(12576878500/1127\) \(54293204876288\) \([2]\) \(2304000\) \(1.6755\) \(\Gamma_0(N)\)-optimal*
464968.b2 464968b1 \([0, 1, 0, -10228, -515040]\) \(-9826000/3703\) \(-44597989719808\) \([2]\) \(1152000\) \(1.3289\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 464968.b1.

Rank

sage: E.rank()
 

The elliptic curves in class 464968.b have rank \(0\).

Complex multiplication

The elliptic curves in class 464968.b do not have complex multiplication.

Modular form 464968.2.a.b

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.