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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 96330c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96330.a4 | 96330c1 | \([1, 1, 0, -321103, 73063333]\) | \(-758575480593601/40535043840\) | \(-195654914422306560\) | \([2]\) | \(1843200\) | \(2.0768\) | \(\Gamma_0(N)\)-optimal |
96330.a3 | 96330c2 | \([1, 1, 0, -5201823, 4564301877]\) | \(3225005357698077121/8526675600\) | \(41156634526160400\) | \([2, 2]\) | \(3686400\) | \(2.4234\) | |
96330.a2 | 96330c3 | \([1, 1, 0, -5266043, 4445738913]\) | \(3345930611358906241/165622259047500\) | \(799427010570804427500\) | \([2]\) | \(7372800\) | \(2.7700\) | |
96330.a1 | 96330c4 | \([1, 1, 0, -83229123, 292219746057]\) | \(13209596798923694545921/92340\) | \(445707543060\) | \([2]\) | \(7372800\) | \(2.7700\) |
Rank
sage: E.rank()
The elliptic curves in class 96330c have rank \(1\).
Complex multiplication
The elliptic curves in class 96330c do not have complex multiplication.Modular form 96330.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.