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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 272734.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 272734.t1 | 272734t3 | \([1, -1, 0, -562286223263, 162287344528684535]\) | \(94330402966367419784492146833/3811688036319086\) | \(794441092686390578777078654\) | \([2]\) | \(1592524800\) | \(5.0983\) | |
| 272734.t2 | 272734t4 | \([1, -1, 0, -38939678003, 1954245810225099]\) | \(31329713901973986300131793/10214846346887693144018\) | \(2129002587861759922658919012657602\) | \([2]\) | \(1592524800\) | \(5.0983\) | |
| 272734.t3 | 272734t2 | \([1, -1, 0, -35144584393, 2535489444214425]\) | \(23033216869836569212815153/4629376217085372676\) | \(964865609492344519639487048164\) | \([2, 2]\) | \(796262400\) | \(4.7517\) | |
| 272734.t4 | 272734t1 | \([1, -1, 0, -1961038613, 48442418385829]\) | \(-4001637980024799157233/2548110404539996912\) | \(-531083235243770787595750285168\) | \([2]\) | \(398131200\) | \(4.4051\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 272734.t have rank \(0\).
Complex multiplication
The elliptic curves in class 272734.t do not have complex multiplication.Modular form 272734.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
