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SageMath
E = EllipticCurve("ik1")
E.isogeny_class()
Elliptic curves in class 91200ik
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.iz4 | 91200ik1 | \([0, 1, 0, -3040033, -2133291937]\) | \(-758575480593601/40535043840\) | \(-166031539568640000000\) | \([2]\) | \(4423680\) | \(2.6388\) | \(\Gamma_0(N)\)-optimal |
| 91200.iz3 | 91200ik2 | \([0, 1, 0, -49248033, -133040555937]\) | \(3225005357698077121/8526675600\) | \(34925263257600000000\) | \([2, 2]\) | \(8847360\) | \(2.9854\) | |
| 91200.iz2 | 91200ik3 | \([0, 1, 0, -49856033, -129587723937]\) | \(3345930611358906241/165622259047500\) | \(678388773058560000000000\) | \([2]\) | \(17694720\) | \(3.3319\) | |
| 91200.iz1 | 91200ik4 | \([0, 1, 0, -787968033, -8513818955937]\) | \(13209596798923694545921/92340\) | \(378224640000000\) | \([2]\) | \(17694720\) | \(3.3319\) |
Rank
sage: E.rank()
The elliptic curves in class 91200ik have rank \(0\).
Complex multiplication
The elliptic curves in class 91200ik do not have complex multiplication.Modular form 91200.2.a.ik
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
