Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 79560.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79560.m1 | 79560g6 | \([0, 0, 0, -324604803, 2251026075998]\) | \(2533559197411478296569602/845325\) | \(1262063462400\) | \([2]\) | \(6291456\) | \(3.0731\) | |
| 79560.m2 | 79560g4 | \([0, 0, 0, -20287803, 35172272198]\) | \(1237089966354690271204/714574355625\) | \(533426898176640000\) | \([2, 2]\) | \(3145728\) | \(2.7265\) | |
| 79560.m3 | 79560g5 | \([0, 0, 0, -20170803, 35597988398]\) | \(-607905111321334101602/14874581985380325\) | \(-22207631907516942182400\) | \([2]\) | \(6291456\) | \(3.0731\) | |
| 79560.m4 | 79560g3 | \([0, 0, 0, -2826723, -1036130578]\) | \(3346154465291614084/1315155029296875\) | \(981757968750000000000\) | \([2]\) | \(3145728\) | \(2.7265\) | |
| 79560.m5 | 79560g2 | \([0, 0, 0, -1275303, 542904698]\) | \(1229125878116884816/29018422265625\) | \(5415534036900000000\) | \([2, 2]\) | \(1572864\) | \(2.3800\) | |
| 79560.m6 | 79560g1 | \([0, 0, 0, 9942, 26493257]\) | \(9317458724864/26001416731875\) | \(-303280524760590000\) | \([2]\) | \(786432\) | \(2.0334\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79560.m have rank \(1\).
Complex multiplication
The elliptic curves in class 79560.m do not have complex multiplication.Modular form 79560.2.a.m
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
