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SageMath
E = EllipticCurve("jn1")
E.isogeny_class()
Elliptic curves in class 100800jn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.mm3 | 100800jn1 | \([0, 0, 0, -74700, -6886000]\) | \(416832723/56000\) | \(6193152000000000\) | \([2]\) | \(442368\) | \(1.7576\) | \(\Gamma_0(N)\)-optimal |
100800.mm4 | 100800jn2 | \([0, 0, 0, 117300, -36454000]\) | \(1613964717/6125000\) | \(-677376000000000000\) | \([2]\) | \(884736\) | \(2.1042\) | |
100800.mm1 | 100800jn3 | \([0, 0, 0, -1514700, 716634000]\) | \(4767078987/6860\) | \(553063956480000000\) | \([2]\) | \(1327104\) | \(2.3069\) | |
100800.mm2 | 100800jn4 | \([0, 0, 0, -1082700, 1133946000]\) | \(-1740992427/5882450\) | \(-474252342681600000000\) | \([2]\) | \(2654208\) | \(2.6535\) |
Rank
sage: E.rank()
The elliptic curves in class 100800jn have rank \(1\).
Complex multiplication
The elliptic curves in class 100800jn do not have complex multiplication.Modular form 100800.2.a.jn
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.