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SageMath
E = EllipticCurve("jd1")
E.isogeny_class()
Elliptic curves in class 95550.jd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95550.jd1 | 95550kb4 | \([1, 0, 0, -2396738, -1428078408]\) | \(828279937799497/193444524\) | \(355602418813687500\) | \([2]\) | \(2359296\) | \(2.3583\) | |
| 95550.jd2 | 95550kb2 | \([1, 0, 0, -167238, -16804908]\) | \(281397674377/96589584\) | \(177557312000250000\) | \([2, 2]\) | \(1179648\) | \(2.0117\) | |
| 95550.jd3 | 95550kb1 | \([1, 0, 0, -69238, 6813092]\) | \(19968681097/628992\) | \(1156254372000000\) | \([2]\) | \(589824\) | \(1.6652\) | \(\Gamma_0(N)\)-optimal |
| 95550.jd4 | 95550kb3 | \([1, 0, 0, 494262, -116691408]\) | \(7264187703863/7406095788\) | \(-13614371302537687500\) | \([2]\) | \(2359296\) | \(2.3583\) |
Rank
sage: E.rank()
The elliptic curves in class 95550.jd have rank \(1\).
Complex multiplication
The elliptic curves in class 95550.jd do not have complex multiplication.Modular form 95550.2.a.jd
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 LMFDB 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 LMFDB labels.
