Properties

Label 101400bl
Number of curves $2$
Conductor $101400$
CM no
Rank $0$
Graph

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

Elliptic curves in class 101400bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101400.by1 101400bl1 \([0, 1, 0, -14083, -299662]\) \(256000/117\) \(141184163250000\) \([2]\) \(387072\) \(1.4100\) \(\Gamma_0(N)\)-optimal
101400.by2 101400bl2 \([0, 1, 0, 49292, -2200912]\) \(686000/507\) \(-9788768652000000\) \([2]\) \(774144\) \(1.7566\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101400bl have rank \(0\).

Complex multiplication

The elliptic curves in class 101400bl do not have complex multiplication.

Modular form 101400.2.a.bl

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