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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 62400de
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.ei4 | 62400de1 | \([0, 1, 0, -229533, -35761437]\) | \(83587439220736/13990184325\) | \(223842949200000000\) | \([2]\) | \(589824\) | \(2.0502\) | \(\Gamma_0(N)\)-optimal |
62400.ei2 | 62400de2 | \([0, 1, 0, -3510033, -2532221937]\) | \(18681746265374416/693005625\) | \(177409440000000000\) | \([2, 2]\) | \(1179648\) | \(2.3968\) | |
62400.ei3 | 62400de3 | \([0, 1, 0, -3348033, -2776355937]\) | \(-4053153720264484/903687890625\) | \(-925376400000000000000\) | \([2]\) | \(2359296\) | \(2.7434\) | |
62400.ei1 | 62400de4 | \([0, 1, 0, -56160033, -162009071937]\) | \(19129597231400697604/26325\) | \(26956800000000\) | \([2]\) | \(2359296\) | \(2.7434\) |
Rank
sage: E.rank()
The elliptic curves in class 62400de have rank \(1\).
Complex multiplication
The elliptic curves in class 62400de do not have complex multiplication.Modular form 62400.2.a.de
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.