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Properties

Label 462462be
Number of curves $2$
Conductor $462462$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("be1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462462be have rank \(0\).

Complex multiplication

The elliptic curves in class 462462be do not have complex multiplication.

Modular form 462462.2.a.be

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} + q^{13} + q^{16} - 6 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 462462be

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462462.be2 462462be1 \([1, 1, 0, 6345, 504981]\) \(1983983375/8805888\) \(-125356473994752\) \([]\) \(1741824\) \(1.3877\) \(\Gamma_0(N)\)-optimal
462462.be1 462462be2 \([1, 1, 0, -58335, -15315747]\) \(-1542230688625/6203396472\) \(-88308630375653688\) \([]\) \(5225472\) \(1.9370\)