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SageMath
E = EllipticCurve("lv1")
E.isogeny_class()
Elliptic curves in class 100800.lv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.lv1 | 100800jr4 | \([0, 0, 0, -1806300, 934362000]\) | \(129348709488/6125\) | \(30862944000000000\) | \([2]\) | \(1327104\) | \(2.2379\) | |
100800.lv2 | 100800jr3 | \([0, 0, 0, -118800, 12987000]\) | \(588791808/109375\) | \(34445250000000000\) | \([2]\) | \(663552\) | \(1.8913\) | |
100800.lv3 | 100800jr2 | \([0, 0, 0, -42300, -1342000]\) | \(1210991472/588245\) | \(4065949440000000\) | \([2]\) | \(442368\) | \(1.6886\) | |
100800.lv4 | 100800jr1 | \([0, 0, 0, -34800, -2497000]\) | \(10788913152/8575\) | \(3704400000000\) | \([2]\) | \(221184\) | \(1.3420\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.lv have rank \(1\).
Complex multiplication
The elliptic curves in class 100800.lv do not have complex multiplication.Modular form 100800.2.a.lv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.