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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 266616m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
266616.m2 | 266616m1 | \([0, 0, 0, -401511, -64363430]\) | \(21296/7\) | \(2352968200050096384\) | \([2]\) | \(2967552\) | \(2.2282\) | \(\Gamma_0(N)\)-optimal |
266616.m1 | 266616m2 | \([0, 0, 0, -2591571, 1557595006]\) | \(1431644/49\) | \(65883109601402698752\) | \([2]\) | \(5935104\) | \(2.5748\) |
Rank
sage: E.rank()
The elliptic curves in class 266616m have rank \(1\).
Complex multiplication
The elliptic curves in class 266616m do not have complex multiplication.Modular form 266616.2.a.m
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.