Properties

Label 64400bt
Number of curves $4$
Conductor $64400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.i3 64400bt1 \([0, 1, 0, -60408, -5568812]\) \(380920459249/12622400\) \(807833600000000\) \([2]\) \(331776\) \(1.6335\) \(\Gamma_0(N)\)-optimal
64400.i4 64400bt2 \([0, 1, 0, 19592, -19168812]\) \(12994449551/2489452840\) \(-159324981760000000\) \([2]\) \(663552\) \(1.9801\)  
64400.i1 64400bt3 \([0, 1, 0, -676408, 212047188]\) \(534774372149809/5323062500\) \(340676000000000000\) \([2]\) \(995328\) \(2.1828\)  
64400.i2 64400bt4 \([0, 1, 0, -176408, 519047188]\) \(-9486391169809/1813439640250\) \(-116060136976000000000\) \([2]\) \(1990656\) \(2.5294\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64400bt have rank \(1\).

Complex multiplication

The elliptic curves in class 64400bt do not have complex multiplication.

Modular form 64400.2.a.bt

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.