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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 333795t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333795.t4 | 333795t1 | \([1, 0, 0, -20817830341, 1124719264057400]\) | \(41336773804526931803116341361/1281566684476192302890625\) | \(30933904274645320568291360390625\) | \([2]\) | \(1436811264\) | \(4.8179\) | \(\Gamma_0(N)\)-optimal |
| 333795.t2 | 333795t2 | \([1, 0, 0, -330566413386, 73153592815625091]\) | \(165503186990359317237822572105281/166746978909722900390625\) | \(4024866708974981279058837890625\) | \([2, 2]\) | \(2873622528\) | \(5.1644\) | |
| 333795.t1 | 333795t3 | \([1, 0, 0, -5289061335261, 4681833639845234466]\) | \(677900562155526557965887564740855281/688129016568984375\) | \(16609761618336003611484375\) | \([2]\) | \(5747245056\) | \(5.5110\) | |
| 333795.t3 | 333795t4 | \([1, 0, 0, -328048820231, 74322692080680120]\) | \(-161750497293247760285958712371601/5257300995290279388427734375\) | \(-126898465527587793767452239990234375\) | \([2]\) | \(5747245056\) | \(5.5110\) |
Rank
sage: E.rank()
The elliptic curves in class 333795t have rank \(1\).
Complex multiplication
The elliptic curves in class 333795t do not have complex multiplication.Modular form 333795.2.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 Cremona 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 Cremona labels.
