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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 48960el
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48960.de3 | 48960el1 | \([0, 0, 0, -58188, 4717712]\) | \(114013572049/15667200\) | \(2994048545587200\) | \([2]\) | \(294912\) | \(1.6964\) | \(\Gamma_0(N)\)-optimal |
| 48960.de2 | 48960el2 | \([0, 0, 0, -242508, -41214832]\) | \(8253429989329/936360000\) | \(178941182607360000\) | \([2, 2]\) | \(589824\) | \(2.0430\) | |
| 48960.de4 | 48960el3 | \([0, 0, 0, 333492, -207333232]\) | \(21464092074671/109596256200\) | \(-20944170718278451200\) | \([2]\) | \(1179648\) | \(2.3896\) | |
| 48960.de1 | 48960el4 | \([0, 0, 0, -3767628, -2814779248]\) | \(30949975477232209/478125000\) | \(91371110400000000\) | \([2]\) | \(1179648\) | \(2.3896\) |
Rank
sage: E.rank()
The elliptic curves in class 48960el have rank \(1\).
Complex multiplication
The elliptic curves in class 48960el do not have complex multiplication.Modular form 48960.2.a.el
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
