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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 217672s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 217672.l3 | 217672s1 | \([0, 0, 0, -1532999, 730568410]\) | \(322440248841552/27209\) | \(33621157396736\) | \([2]\) | \(1505280\) | \(2.0376\) | \(\Gamma_0(N)\)-optimal |
| 217672.l2 | 217672s2 | \([0, 0, 0, -1536379, 727185030]\) | \(81144432781668/740329681\) | \(3659192286431159296\) | \([2, 2]\) | \(3010560\) | \(2.3841\) | |
| 217672.l4 | 217672s3 | \([0, 0, 0, -448019, 1737400782]\) | \(-1006057824354/131332646081\) | \(-1298263240903855163392\) | \([2]\) | \(6021120\) | \(2.7307\) | |
| 217672.l1 | 217672s4 | \([0, 0, 0, -2678819, -499567042]\) | \(215062038362754/113550802729\) | \(1122484298894462486528\) | \([2]\) | \(6021120\) | \(2.7307\) |
Rank
sage: E.rank()
The elliptic curves in class 217672s have rank \(0\).
Complex multiplication
The elliptic curves in class 217672s do not have complex multiplication.Modular form 217672.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
