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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 48672s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48672.l3 | 48672s1 | \([0, 0, 0, -356421, -81508700]\) | \(22235451328/123201\) | \(27744816006333504\) | \([2, 2]\) | \(516096\) | \(1.9979\) | \(\Gamma_0(N)\)-optimal |
| 48672.l4 | 48672s2 | \([0, 0, 0, -158691, -171475850]\) | \(-245314376/6908733\) | \(-12446751303764384256\) | \([2]\) | \(1032192\) | \(2.3445\) | |
| 48672.l2 | 48672s3 | \([0, 0, 0, -561756, 23130016]\) | \(1360251712/771147\) | \(11114367774981599232\) | \([2]\) | \(1032192\) | \(2.3445\) | |
| 48672.l1 | 48672s4 | \([0, 0, 0, -5695131, -5231228366]\) | \(11339065490696/351\) | \(632360478776832\) | \([2]\) | \(1032192\) | \(2.3445\) |
Rank
sage: E.rank()
The elliptic curves in class 48672s have rank \(0\).
Complex multiplication
The elliptic curves in class 48672s do not have complex multiplication.Modular form 48672.2.a.s
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
