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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 8112q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8112.q1 | 8112q1 | \([0, 1, 0, -110075, -13242696]\) | \(1909913257984/129730653\) | \(10018961335620432\) | \([2]\) | \(80640\) | \(1.8189\) | \(\Gamma_0(N)\)-optimal |
| 8112.q2 | 8112q2 | \([0, 1, 0, 95260, -56773716]\) | \(77366117936/1172914587\) | \(-1449327279299298048\) | \([2]\) | \(161280\) | \(2.1654\) |
Rank
sage: E.rank()
The elliptic curves in class 8112q have rank \(0\).
Complex multiplication
The elliptic curves in class 8112q do not have complex multiplication.Modular form 8112.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
