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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 256025.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 256025.c1 | 256025c4 | \([1, -1, 1, -1245566755, 14884330223872]\) | \(116256292809537371612841/15216540068579856875\) | \(27972042539505493460732421875\) | \([2]\) | \(162791424\) | \(4.1866\) | |
| 256025.c2 | 256025c2 | \([1, -1, 1, -1203457380, 16069203817622]\) | \(104859453317683374662841/2223652969140625\) | \(4087664815100396728515625\) | \([2, 2]\) | \(81395712\) | \(3.8401\) | |
| 256025.c3 | 256025c1 | \([1, -1, 1, -1203451255, 16069375562622]\) | \(104857852278310619039721/47155625\) | \(86684564462890625\) | \([2]\) | \(40697856\) | \(3.4935\) | \(\Gamma_0(N)\)-optimal |
| 256025.c4 | 256025c3 | \([1, -1, 1, -1161446005, 17243085657872]\) | \(-94256762600623910012361/15323275604248046875\) | \(-28168250805690288543701171875\) | \([2]\) | \(162791424\) | \(4.1866\) |
Rank
sage: E.rank()
The elliptic curves in class 256025.c have rank \(0\).
Complex multiplication
The elliptic curves in class 256025.c do not have complex multiplication.Modular form 256025.2.a.c
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.
