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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 2730.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2730.m1 | 2730p5 | \([1, 0, 1, -852274, -302906428]\) | \(68463752473882049153689/1817088000000000\) | \(1817088000000000\) | \([2]\) | \(46656\) | \(2.0333\) | |
2730.m2 | 2730p6 | \([1, 0, 1, -818994, -327640124]\) | \(-60752633741424905775769/11197265625000000000\) | \(-11197265625000000000\) | \([2]\) | \(93312\) | \(2.3798\) | |
2730.m3 | 2730p3 | \([1, 0, 1, -18259, 270446]\) | \(673163386034885929/357608625192000\) | \(357608625192000\) | \([6]\) | \(15552\) | \(1.4840\) | |
2730.m4 | 2730p1 | \([1, 0, 1, -14344, 660002]\) | \(326355561310674169/465699780\) | \(465699780\) | \([6]\) | \(5184\) | \(0.93465\) | \(\Gamma_0(N)\)-optimal |
2730.m5 | 2730p2 | \([1, 0, 1, -14214, 672586]\) | \(-317562142497484249/12339342574650\) | \(-12339342574650\) | \([6]\) | \(10368\) | \(1.2812\) | |
2730.m6 | 2730p4 | \([1, 0, 1, 69621, 2133502]\) | \(37321015309599759191/23553520979625000\) | \(-23553520979625000\) | \([6]\) | \(31104\) | \(1.8305\) |
Rank
sage: E.rank()
The elliptic curves in class 2730.m have rank \(0\).
Complex multiplication
The elliptic curves in class 2730.m do not have complex multiplication.Modular form 2730.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.