Properties

Label 2800.bd
Number of curves $2$
Conductor $2800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2800.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.bd1 2800g2 \([0, -1, 0, -1008, 12512]\) \(3543122/49\) \(1568000000\) \([2]\) \(1280\) \(0.57005\)  
2800.bd2 2800g1 \([0, -1, 0, -8, 512]\) \(-4/7\) \(-112000000\) \([2]\) \(640\) \(0.22348\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2800.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 2800.bd do not have complex multiplication.

Modular form 2800.2.a.bd

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{7} + q^{9} + 2q^{17} + 2q^{19} + O(q^{20})\)  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.