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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 7920.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7920.t1 | 7920bi3 | \([0, 0, 0, -263938467, -1650339826526]\) | \(680995599504466943307169/52207031250000000\) | \(155889360000000000000000\) | \([2]\) | \(1720320\) | \(3.4985\) | |
| 7920.t2 | 7920bi2 | \([0, 0, 0, -17594787, -22155907934]\) | \(201738262891771037089/45727545600000000\) | \(136541719520870400000000\) | \([2, 2]\) | \(860160\) | \(3.1519\) | |
| 7920.t3 | 7920bi1 | \([0, 0, 0, -5798307, 5077445794]\) | \(7220044159551112609/448454983680000\) | \(1339079405988741120000\) | \([2]\) | \(430080\) | \(2.8054\) | \(\Gamma_0(N)\)-optimal |
| 7920.t4 | 7920bi4 | \([0, 0, 0, 40005213, -136906627934]\) | \(2371297246710590562911/4084000833203280000\) | \(-12194761143931662827520000\) | \([2]\) | \(1720320\) | \(3.4985\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.t have rank \(0\).
Complex multiplication
The elliptic curves in class 7920.t do not have complex multiplication.Modular form 7920.2.a.t
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.
