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SageMath
E = EllipticCurve("in1")
E.isogeny_class()
Elliptic curves in class 248430.in
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
248430.in1 | 248430in3 | \([1, 0, 0, -4004036, 3082981446]\) | \(12501706118329/2570490\) | \(1459702233678870090\) | \([2]\) | \(8257536\) | \(2.4825\) | |
248430.in2 | 248430in2 | \([1, 0, 0, -277586, 36981216]\) | \(4165509529/1368900\) | \(777356219118924900\) | \([2, 2]\) | \(4128768\) | \(2.1359\) | |
248430.in3 | 248430in1 | \([1, 0, 0, -111966, -13996620]\) | \(273359449/9360\) | \(5315256199103760\) | \([2]\) | \(2064384\) | \(1.7893\) | \(\Gamma_0(N)\)-optimal |
248430.in4 | 248430in4 | \([1, 0, 0, 798944, 254224970]\) | \(99317171591/106616250\) | \(-60544090142916266250\) | \([2]\) | \(8257536\) | \(2.4825\) |
Rank
sage: E.rank()
The elliptic curves in class 248430.in have rank \(0\).
Complex multiplication
The elliptic curves in class 248430.in do not have complex multiplication.Modular form 248430.2.a.in
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.