Properties

Label 62400.bl
Number of curves $2$
Conductor $62400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.bl1 62400n2 \([0, -1, 0, -73633, -6864863]\) \(10779215329/1232010\) \(5046312960000000\) \([2]\) \(442368\) \(1.7454\)  
62400.bl2 62400n1 \([0, -1, 0, 6367, -544863]\) \(6967871/35100\) \(-143769600000000\) \([2]\) \(221184\) \(1.3988\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62400.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 62400.bl do not have complex multiplication.

Modular form 62400.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} - 4q^{11} - q^{13} - 8q^{17} + 6q^{19} + O(q^{20})\)  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.