Properties

Label 250096bl
Number of curves $4$
Conductor $250096$
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 250096bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250096.bl4 250096bl1 \([0, 0, 0, 458101, 136022138]\) \(22062729659823/29354283343\) \(-14145544523860406272\) \([2]\) \(4128768\) \(2.3605\) \(\Gamma_0(N)\)-optimal
250096.bl3 250096bl2 \([0, 0, 0, -2838619, 1331412810]\) \(5249244962308257/1448621666569\) \(698076735283922046976\) \([2, 2]\) \(8257536\) \(2.7071\)  
250096.bl1 250096bl3 \([0, 0, 0, -41830859, 104122755898]\) \(16798320881842096017/2132227789307\) \(1027499897586398179328\) \([4]\) \(16515072\) \(3.0536\)  
250096.bl2 250096bl4 \([0, 0, 0, -16593899, -24954927270]\) \(1048626554636928177/48569076788309\) \(23404967178517567655936\) \([2]\) \(16515072\) \(3.0536\)  

Rank

sage: E.rank()
 

The elliptic curves in class 250096bl have rank \(1\).

Complex multiplication

The elliptic curves in class 250096bl do not have complex multiplication.

Modular form 250096.2.a.bl

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - 3q^{9} + q^{11} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.