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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 308550d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.d2 | 308550d1 | \([1, 1, 0, -1420051525, 20580847298125]\) | \(8595711443128766579/7520256000000\) | \(277068285483264000000000000\) | \([2]\) | \(273715200\) | \(3.9996\) | \(\Gamma_0(N)\)-optimal |
308550.d1 | 308550d2 | \([1, 1, 0, -22716051525, 1317784095298125]\) | \(35185850652034529726579/26967168000\) | \(993549554975142000000000\) | \([2]\) | \(547430400\) | \(4.3462\) |
Rank
sage: E.rank()
The elliptic curves in class 308550d have rank \(1\).
Complex multiplication
The elliptic curves in class 308550d do not have complex multiplication.Modular form 308550.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.