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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 102966q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102966.q4 | 102966q1 | \([1, 1, 1, -506607, -20956491]\) | \(2845178713/1609728\) | \(8135425497917165568\) | \([4]\) | \(2471040\) | \(2.3185\) | \(\Gamma_0(N)\)-optimal |
| 102966.q2 | 102966q2 | \([1, 1, 1, -5998127, -5646469579]\) | \(4722184089433/9884736\) | \(49956597198147594816\) | \([2, 2]\) | \(4942080\) | \(2.6651\) | |
| 102966.q3 | 102966q3 | \([1, 1, 1, -3938807, -9579770779]\) | \(-1337180541913/7067998104\) | \(-35721048521558786443224\) | \([2]\) | \(9884160\) | \(3.0117\) | |
| 102966.q1 | 102966q4 | \([1, 1, 1, -95921767, -361636175611]\) | \(19312898130234073/84888\) | \(429016578991725528\) | \([2]\) | \(9884160\) | \(3.0117\) |
Rank
sage: E.rank()
The elliptic curves in class 102966q have rank \(1\).
Complex multiplication
The elliptic curves in class 102966q do not have complex multiplication.Modular form 102966.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
