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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 22308f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22308.e4 | 22308f1 | \([0, 1, 0, -16084293, -24460308144]\) | \(5958673237147648000/102990700534293\) | \(7953863044083684176592\) | \([2]\) | \(1306368\) | \(2.9994\) | \(\Gamma_0(N)\)-optimal |
| 22308.e3 | 22308f2 | \([0, 1, 0, -32716428, 34763398164]\) | \(3134160907827154000/1390984039929627\) | \(1718787656393902840382208\) | \([2]\) | \(2612736\) | \(3.3459\) | |
| 22308.e2 | 22308f3 | \([0, 1, 0, -1297374693, -17986915270908]\) | \(3127086412733145284608000/16789083597\) | \(1296603196924031568\) | \([2]\) | \(3919104\) | \(3.5487\) | |
| 22308.e1 | 22308f4 | \([0, 1, 0, -1297397508, -17986251044124]\) | \(195453211868372997250000/14320648682977923\) | \(17695497202902012297652992\) | \([2]\) | \(7838208\) | \(3.8952\) |
Rank
sage: E.rank()
The elliptic curves in class 22308f have rank \(0\).
Complex multiplication
The elliptic curves in class 22308f do not have complex multiplication.Modular form 22308.2.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.
