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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 250096.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250096.bl1 | 250096bl3 | \([0, 0, 0, -41830859, 104122755898]\) | \(16798320881842096017/2132227789307\) | \(1027499897586398179328\) | \([4]\) | \(16515072\) | \(3.0536\) | |
| 250096.bl2 | 250096bl4 | \([0, 0, 0, -16593899, -24954927270]\) | \(1048626554636928177/48569076788309\) | \(23404967178517567655936\) | \([2]\) | \(16515072\) | \(3.0536\) | |
| 250096.bl3 | 250096bl2 | \([0, 0, 0, -2838619, 1331412810]\) | \(5249244962308257/1448621666569\) | \(698076735283922046976\) | \([2, 2]\) | \(8257536\) | \(2.7071\) | |
| 250096.bl4 | 250096bl1 | \([0, 0, 0, 458101, 136022138]\) | \(22062729659823/29354283343\) | \(-14145544523860406272\) | \([2]\) | \(4128768\) | \(2.3605\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 250096.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 250096.bl do not have complex multiplication.Modular form 250096.2.a.bl
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
