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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 15162l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15162.j5 | 15162l1 | \([1, 0, 1, -1452, -47126]\) | \(-7189057/16128\) | \(-758755968768\) | \([2]\) | \(27648\) | \(0.96817\) | \(\Gamma_0(N)\)-optimal |
15162.j4 | 15162l2 | \([1, 0, 1, -30332, -2034070]\) | \(65597103937/63504\) | \(2987601627024\) | \([2, 2]\) | \(55296\) | \(1.3147\) | |
15162.j1 | 15162l3 | \([1, 0, 1, -485192, -130122646]\) | \(268498407453697/252\) | \(11855562012\) | \([2]\) | \(110592\) | \(1.6613\) | |
15162.j3 | 15162l4 | \([1, 0, 1, -37552, -994390]\) | \(124475734657/63011844\) | \(2964447714414564\) | \([2, 2]\) | \(110592\) | \(1.6613\) | |
15162.j2 | 15162l5 | \([1, 0, 1, -329962, 72225074]\) | \(84448510979617/933897762\) | \(43936042977218322\) | \([2]\) | \(221184\) | \(2.0079\) | |
15162.j6 | 15162l6 | \([1, 0, 1, 139338, -7645454]\) | \(6359387729183/4218578658\) | \(-198466749533407698\) | \([2]\) | \(221184\) | \(2.0079\) |
Rank
sage: E.rank()
The elliptic curves in class 15162l have rank \(1\).
Complex multiplication
The elliptic curves in class 15162l do not have complex multiplication.Modular form 15162.2.a.l
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.