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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 117208.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117208.l1 | 117208r4 | \([0, 0, 0, -776699, 77993398]\) | \(215062038362754/113550802729\) | \(27359515423260919808\) | \([2]\) | \(1720320\) | \(2.4212\) | |
| 117208.l2 | 117208r2 | \([0, 0, 0, -445459, -113529570]\) | \(81144432781668/740329681\) | \(89189423759328256\) | \([2, 2]\) | \(860160\) | \(2.0746\) | |
| 117208.l3 | 117208r1 | \([0, 0, 0, -444479, -114057790]\) | \(322440248841552/27209\) | \(819484580096\) | \([2]\) | \(430080\) | \(1.7280\) | \(\Gamma_0(N)\)-optimal |
| 117208.l4 | 117208r3 | \([0, 0, 0, -129899, -271246458]\) | \(-1006057824354/131332646081\) | \(-31643964372548749312\) | \([2]\) | \(1720320\) | \(2.4212\) |
Rank
sage: E.rank()
The elliptic curves in class 117208.l have rank \(0\).
Complex multiplication
The elliptic curves in class 117208.l do not have complex multiplication.Modular form 117208.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
