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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 79350t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79350.f4 | 79350t1 | \([1, 1, 0, -39950, 4164000]\) | \(-24389/12\) | \(-3469591148437500\) | \([2]\) | \(492800\) | \(1.6872\) | \(\Gamma_0(N)\)-optimal |
| 79350.f2 | 79350t2 | \([1, 1, 0, -701200, 225682750]\) | \(131872229/18\) | \(5204386722656250\) | \([2]\) | \(985600\) | \(2.0338\) | |
| 79350.f3 | 79350t3 | \([1, 1, 0, -370575, -417382875]\) | \(-19465109/248832\) | \(-71945442054000000000\) | \([2]\) | \(2464000\) | \(2.4919\) | |
| 79350.f1 | 79350t4 | \([1, 1, 0, -10950575, -13906882875]\) | \(502270291349/1889568\) | \(546335700597562500000\) | \([2]\) | \(4928000\) | \(2.8385\) |
Rank
sage: E.rank()
The elliptic curves in class 79350t have rank \(1\).
Complex multiplication
The elliptic curves in class 79350t do not have complex multiplication.Modular form 79350.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
