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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 102960.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.n1 | 102960cb4 | \([0, 0, 0, -11148003, 12723414498]\) | \(1900481745258486963/232375000000000\) | \(18734436864000000000000\) | \([2]\) | \(7962624\) | \(3.0040\) | |
| 102960.n2 | 102960cb2 | \([0, 0, 0, -2670963, -1677708238]\) | \(19054765821218746347/32122413895000\) | \(3552481997475840000\) | \([2]\) | \(2654208\) | \(2.4547\) | |
| 102960.n3 | 102960cb1 | \([0, 0, 0, -115443, -42686542]\) | \(-1538518817843307/6227391227200\) | \(-688699650598502400\) | \([2]\) | \(1327104\) | \(2.1081\) | \(\Gamma_0(N)\)-optimal |
| 102960.n4 | 102960cb3 | \([0, 0, 0, 1017117, 1023002082]\) | \(1443395048293197/6443008000000\) | \(-519445407596544000000\) | \([2]\) | \(3981312\) | \(2.6574\) |
Rank
sage: E.rank()
The elliptic curves in class 102960.n have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.n do not have complex multiplication.Modular form 102960.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
