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SageMath
E = EllipticCurve("ox1")
E.isogeny_class()
Elliptic curves in class 141120.ox
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.ox1 | 141120kb3 | \([0, 0, 0, -571564812, 5259522722384]\) | \(7347751505995469192/72930375\) | \(204962377460133888000\) | \([2]\) | \(23592960\) | \(3.4737\) | |
141120.ox2 | 141120kb4 | \([0, 0, 0, -51184812, 4300358384]\) | \(5276930158229192/3050936350875\) | \(8574303477184715354112000\) | \([2]\) | \(23592960\) | \(3.4737\) | |
141120.ox3 | 141120kb2 | \([0, 0, 0, -35749812, 82049540384]\) | \(14383655824793536/45209390625\) | \(15881969937121344000000\) | \([2, 2]\) | \(11796480\) | \(3.1271\) | |
141120.ox4 | 141120kb1 | \([0, 0, 0, -1296687, 2366352884]\) | \(-43927191786304/415283203125\) | \(-2279502684703125000000\) | \([2]\) | \(5898240\) | \(2.7806\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.ox have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.ox do not have complex multiplication.Modular form 141120.2.a.ox
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.