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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 248256.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248256.t1 | 248256t3 | \([0, 0, 0, -42447756, 106444979984]\) | \(44260923429070723297/593700376032\) | \(113457908712034271232\) | \([2]\) | \(16220160\) | \(2.9911\) | |
| 248256.t2 | 248256t4 | \([0, 0, 0, -10191756, -10829062384]\) | \(612637130696707297/89442530521632\) | \(17092733763654707576832\) | \([2]\) | \(16220160\) | \(2.9911\) | |
| 248256.t3 | 248256t2 | \([0, 0, 0, -2726796, 1565757200]\) | \(11733138754458337/1248028591104\) | \(238501977893061525504\) | \([2, 2]\) | \(8110080\) | \(2.6445\) | |
| 248256.t4 | 248256t1 | \([0, 0, 0, 222324, 120688400]\) | \(6359387729183/36606836736\) | \(-6995675442195726336\) | \([2]\) | \(4055040\) | \(2.2980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 248256.t have rank \(1\).
Complex multiplication
The elliptic curves in class 248256.t do not have complex multiplication.Modular form 248256.2.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.
