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Properties

Label 2450.bf
Number of curves $2$
Conductor $2450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 2450.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2450.bf1 2450u2 \([1, 1, 1, -194188, -57275219]\) \(-8990558521/10485760\) \(-944504995840000000\) \([]\) \(42336\) \(2.1432\)  
2450.bf2 2450u1 \([1, 1, 1, 20187, 1463531]\) \(10100279/16000\) \(-1441200250000000\) \([]\) \(14112\) \(1.5939\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2450.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 2450.bf do not have complex multiplication.

Modular form 2450.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{8} + q^{9} + 3 q^{11} + 2 q^{12} + q^{13} + q^{16} + 6 q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.