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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 15210.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.o1 | 15210u4 | \([1, -1, 0, -1327190409, 18610273870605]\) | \(73474353581350183614361/576510977802240\) | \(2028594406289641491824640\) | \([2]\) | \(5806080\) | \(3.8372\) | |
| 15210.o2 | 15210u3 | \([1, -1, 0, -81187209, 303745655565]\) | \(-16818951115904497561/1592332281446400\) | \(-5603009280778416055910400\) | \([2]\) | \(2903040\) | \(3.4906\) | |
| 15210.o3 | 15210u2 | \([1, -1, 0, -24339834, -1733847660]\) | \(453198971846635561/261896250564000\) | \(921545797701367731204000\) | \([2]\) | \(1935360\) | \(3.2879\) | |
| 15210.o4 | 15210u1 | \([1, -1, 0, 6080166, -218931660]\) | \(7064514799444439/4094064000000\) | \(-14405962157134704000000\) | \([2]\) | \(967680\) | \(2.9413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15210.o have rank \(1\).
Complex multiplication
The elliptic curves in class 15210.o do not have complex multiplication.Modular form 15210.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
