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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 116610.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116610.o1 | 116610i4 | \([1, 1, 0, -233627462, -1374563187564]\) | \(292169767125103365085489/72534787200\) | \(350111563670044800\) | \([2]\) | \(13762560\) | \(3.1821\) | |
| 116610.o2 | 116610i3 | \([1, 1, 0, -17091142, -13663912556]\) | \(114387056741228939569/49503729150000000\) | \(238945045394782350000000\) | \([2]\) | \(13762560\) | \(3.1821\) | |
| 116610.o3 | 116610i2 | \([1, 1, 0, -14603462, -21476720364]\) | \(71356102305927901489/35540674560000\) | \(171548047832279040000\) | \([2, 2]\) | \(6881280\) | \(2.8355\) | |
| 116610.o4 | 116610i1 | \([1, 1, 0, -758982, -452493036]\) | \(-10017490085065009/12502381363200\) | \(-60346606885326028800\) | \([2]\) | \(3440640\) | \(2.4890\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116610.o have rank \(0\).
Complex multiplication
The elliptic curves in class 116610.o do not have complex multiplication.Modular form 116610.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
