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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 98838.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98838.k1 | 98838q3 | \([1, -1, 0, -1113282, 452396992]\) | \(8671983378625/82308\) | \(1448315256324708\) | \([2]\) | \(1327104\) | \(2.0714\) | |
| 98838.k2 | 98838q4 | \([1, -1, 0, -1087272, 474521098]\) | \(-8078253774625/846825858\) | \(-14900991514696758258\) | \([2]\) | \(2654208\) | \(2.4180\) | |
| 98838.k3 | 98838q1 | \([1, -1, 0, -20862, -83372]\) | \(57066625/32832\) | \(577721321082432\) | \([2]\) | \(442368\) | \(1.5221\) | \(\Gamma_0(N)\)-optimal |
| 98838.k4 | 98838q2 | \([1, -1, 0, 83178, -728420]\) | \(3616805375/2105352\) | \(-37046379714410952\) | \([2]\) | \(884736\) | \(1.8687\) |
Rank
sage: E.rank()
The elliptic curves in class 98838.k have rank \(1\).
Complex multiplication
The elliptic curves in class 98838.k do not have complex multiplication.Modular form 98838.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
