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SageMath
E = EllipticCurve("ju1")
E.isogeny_class()
Elliptic curves in class 58800ju
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.hb4 | 58800ju1 | \([0, 1, 0, -2368, -61132]\) | \(-24389/12\) | \(-722835456000\) | \([2]\) | \(69120\) | \(0.98083\) | \(\Gamma_0(N)\)-optimal |
| 58800.hb2 | 58800ju2 | \([0, 1, 0, -41568, -3275532]\) | \(131872229/18\) | \(1084253184000\) | \([2]\) | \(138240\) | \(1.3274\) | |
| 58800.hb3 | 58800ju3 | \([0, 1, 0, -21968, 6014868]\) | \(-19465109/248832\) | \(-14988716015616000\) | \([2]\) | \(345600\) | \(1.7855\) | |
| 58800.hb1 | 58800ju4 | \([0, 1, 0, -649168, 200446868]\) | \(502270291349/1889568\) | \(113820562243584000\) | \([2]\) | \(691200\) | \(2.1321\) |
Rank
sage: E.rank()
The elliptic curves in class 58800ju have rank \(1\).
Complex multiplication
The elliptic curves in class 58800ju do not have complex multiplication.Modular form 58800.2.a.ju
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
