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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 98736cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.bl3 | 98736cg1 | \([0, -1, 0, -397747368, -3022263827856]\) | \(959024269496848362625/11151660319506432\) | \(80919947293839909602721792\) | \([2]\) | \(33177600\) | \(3.7837\) | \(\Gamma_0(N)\)-optimal |
| 98736.bl4 | 98736cg2 | \([0, -1, 0, -80553128, -7710140939664]\) | \(-7966267523043306625/3534510366354604032\) | \(-25647516545554549446795067392\) | \([2]\) | \(66355200\) | \(4.1303\) | |
| 98736.bl1 | 98736cg3 | \([0, -1, 0, -32127083688, -2216424652946832]\) | \(505384091400037554067434625/815656731648\) | \(5918661243597056114688\) | \([2]\) | \(99532800\) | \(4.3330\) | |
| 98736.bl2 | 98736cg4 | \([0, -1, 0, -32126773928, -2216469530480016]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-147326534597291929857814560768\) | \([2]\) | \(199065600\) | \(4.6796\) |
Rank
sage: E.rank()
The elliptic curves in class 98736cg have rank \(0\).
Complex multiplication
The elliptic curves in class 98736cg do not have complex multiplication.Modular form 98736.2.a.cg
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.
