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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 6160.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6160.e1 | 6160j4 | \([0, 0, 0, -334547, 74478994]\) | \(1010962818911303721/57392720\) | \(235080581120\) | \([4]\) | \(24576\) | \(1.6485\) | |
| 6160.e2 | 6160j3 | \([0, 0, 0, -35027, -595054]\) | \(1160306142246441/634128110000\) | \(2597388738560000\) | \([2]\) | \(24576\) | \(1.6485\) | |
| 6160.e3 | 6160j2 | \([0, 0, 0, -20947, 1159314]\) | \(248158561089321/1859334400\) | \(7615833702400\) | \([2, 2]\) | \(12288\) | \(1.3020\) | |
| 6160.e4 | 6160j1 | \([0, 0, 0, -467, 41106]\) | \(-2749884201/176619520\) | \(-723433553920\) | \([2]\) | \(6144\) | \(0.95539\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6160.e have rank \(0\).
Complex multiplication
The elliptic curves in class 6160.e do not have complex multiplication.Modular form 6160.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
