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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 13860f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13860.t3 | 13860f1 | \([0, 0, 0, -1032, -1031]\) | \(281370820608/161767375\) | \(69883506000\) | \([6]\) | \(10368\) | \(0.77046\) | \(\Gamma_0(N)\)-optimal |
| 13860.t4 | 13860f2 | \([0, 0, 0, 4113, -8234]\) | \(1113258734352/648484375\) | \(-4482324000000\) | \([6]\) | \(20736\) | \(1.1170\) | |
| 13860.t1 | 13860f3 | \([0, 0, 0, -59832, -5633091]\) | \(75216478666752/326095\) | \(102696446160\) | \([2]\) | \(31104\) | \(1.3198\) | |
| 13860.t2 | 13860f4 | \([0, 0, 0, -58887, -5819634]\) | \(-4481782160112/310023175\) | \(-1562159655302400\) | \([2]\) | \(62208\) | \(1.6663\) |
Rank
sage: E.rank()
The elliptic curves in class 13860f have rank \(0\).
Complex multiplication
The elliptic curves in class 13860f do not have complex multiplication.Modular form 13860.2.a.f
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.
