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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 26010t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26010.p4 | 26010t1 | \([1, -1, 0, 64971, 50004085]\) | \(1723683599/62424000\) | \(-1098430669689624000\) | \([2]\) | \(331776\) | \(2.1416\) | \(\Gamma_0(N)\)-optimal |
| 26010.p3 | 26010t2 | \([1, -1, 0, -1703709, 818672413]\) | \(31080575499121/1549125000\) | \(27258849339724125000\) | \([2]\) | \(663552\) | \(2.4882\) | |
| 26010.p2 | 26010t3 | \([1, -1, 0, -8518329, 9574501945]\) | \(-3884775383991601/1448254140\) | \(-25483896656429746140\) | \([2]\) | \(995328\) | \(2.6909\) | |
| 26010.p1 | 26010t4 | \([1, -1, 0, -136305459, 612550853563]\) | \(15916310615119911121/2210850\) | \(38902752884840850\) | \([2]\) | \(1990656\) | \(3.0375\) |
Rank
sage: E.rank()
The elliptic curves in class 26010t have rank \(1\).
Complex multiplication
The elliptic curves in class 26010t do not have complex multiplication.Modular form 26010.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
