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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 193200.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.v1 | 193200ep4 | \([0, -1, 0, -337089408, -2382002258688]\) | \(66187969564358252770489/550144842789780\) | \(35209269938545920000000\) | \([2]\) | \(35389440\) | \(3.4961\) | |
| 193200.v2 | 193200ep2 | \([0, -1, 0, -21529408, -35498098688]\) | \(17244079743478944889/1469997007491600\) | \(94079808479462400000000\) | \([2, 2]\) | \(17694720\) | \(3.1495\) | |
| 193200.v3 | 193200ep1 | \([0, -1, 0, -4601408, 3165453312]\) | \(168351140229842809/29855318411520\) | \(1910740378337280000000\) | \([2]\) | \(8847360\) | \(2.8029\) | \(\Gamma_0(N)\)-optimal |
| 193200.v4 | 193200ep3 | \([0, -1, 0, 23182592, -163732114688]\) | \(21529289381199961031/193397385415972500\) | \(-12377432666622240000000000\) | \([2]\) | \(35389440\) | \(3.4961\) |
Rank
sage: E.rank()
The elliptic curves in class 193200.v have rank \(0\).
Complex multiplication
The elliptic curves in class 193200.v do not have complex multiplication.Modular form 193200.2.a.v
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.
