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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 17136.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17136.bl1 | 17136j4 | \([0, 0, 0, -1632306819, 25383459170018]\) | \(322159999717985454060440834/4250799\) | \(6346408900608\) | \([2]\) | \(2211840\) | \(3.4403\) | |
17136.bl2 | 17136j3 | \([0, 0, 0, -102281619, 394473389042]\) | \(79260902459030376659234/842751810121431609\) | \(1258221710496816420784128\) | \([2]\) | \(2211840\) | \(3.4403\) | |
17136.bl3 | 17136j2 | \([0, 0, 0, -102019179, 396616526570]\) | \(157304700372188331121828/18069292138401\) | \(13488654304147792896\) | \([2, 2]\) | \(1105920\) | \(3.0937\) | |
17136.bl4 | 17136j1 | \([0, 0, 0, -6359799, 6230596790]\) | \(-152435594466395827792/1646846627220711\) | \(-307341104958437969664\) | \([2]\) | \(552960\) | \(2.7472\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17136.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 17136.bl do not have complex multiplication.Modular form 17136.2.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.