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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 121275ge
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.e2 | 121275ge1 | \([0, 0, 1, -383563425, -2891371495644]\) | \(116423188793017446400/91315917\) | \(4894882491654973125\) | \([]\) | \(20275200\) | \(3.3263\) | \(\Gamma_0(N)\)-optimal |
| 121275.e1 | 121275ge2 | \([0, 0, 1, -744720375, 3346254352656]\) | \(1363413585016606720/644626239703677\) | \(21596520341484595987076953125\) | \([]\) | \(101376000\) | \(4.1310\) |
Rank
sage: E.rank()
The elliptic curves in class 121275ge have rank \(0\).
Complex multiplication
The elliptic curves in class 121275ge do not have complex multiplication.Modular form 121275.2.a.ge
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
