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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 79560f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79560.l4 | 79560f1 | \([0, 0, 0, -149178, -22177127]\) | \(31476797652269056/49725\) | \(579992400\) | \([2]\) | \(180224\) | \(1.3760\) | \(\Gamma_0(N)\)-optimal |
| 79560.l3 | 79560f2 | \([0, 0, 0, -149223, -22163078]\) | \(1969080716416336/2472575625\) | \(461441953440000\) | \([2, 2]\) | \(360448\) | \(1.7225\) | |
| 79560.l5 | 79560f3 | \([0, 0, 0, -109443, -34248242]\) | \(-194204905090564/566398828125\) | \(-422814459600000000\) | \([2]\) | \(720896\) | \(2.0691\) | |
| 79560.l2 | 79560f4 | \([0, 0, 0, -189723, -9178778]\) | \(1011710313226084/536724738225\) | \(400662870186009600\) | \([2, 2]\) | \(720896\) | \(2.0691\) | |
| 79560.l6 | 79560f5 | \([0, 0, 0, 722877, -71783138]\) | \(27980756504588158/17683545112935\) | \(-26401391385251051520\) | \([2]\) | \(1441792\) | \(2.4157\) | |
| 79560.l1 | 79560f6 | \([0, 0, 0, -1750323, 884420782]\) | \(397210600760070242/3536192675535\) | \(5279507375032350720\) | \([2]\) | \(1441792\) | \(2.4157\) |
Rank
sage: E.rank()
The elliptic curves in class 79560f have rank \(1\).
Complex multiplication
The elliptic curves in class 79560f do not have complex multiplication.Modular form 79560.2.a.f
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
