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SageMath
E = EllipticCurve("is1")
E.isogeny_class()
Elliptic curves in class 270480is
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.is3 | 270480is1 | \([0, 1, 0, -99664840, 410132431988]\) | \(-227196402372228188089/19338934824115200\) | \(-9319245181429060259020800\) | \([2]\) | \(53084160\) | \(3.5360\) | \(\Gamma_0(N)\)-optimal |
| 270480.is2 | 270480is2 | \([0, 1, 0, -1625893320, 25233322922100]\) | \(986396822567235411402169/6336721794060000\) | \(3053604791702998794240000\) | \([2]\) | \(106168320\) | \(3.8826\) | |
| 270480.is4 | 270480is3 | \([0, 1, 0, 590870600, 15362652500]\) | \(47342661265381757089751/27397579603968000000\) | \(-13202627964220339126272000000\) | \([2]\) | \(159252480\) | \(4.0853\) | |
| 270480.is1 | 270480is4 | \([0, 1, 0, -2363492280, 120537971028]\) | \(3029968325354577848895529/1753440696000000000000\) | \(844966070041411584000000000000\) | \([2]\) | \(318504960\) | \(4.4319\) |
Rank
sage: E.rank()
The elliptic curves in class 270480is have rank \(1\).
Complex multiplication
The elliptic curves in class 270480is do not have complex multiplication.Modular form 270480.2.a.is
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
