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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 35280.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.bj1 | 35280dy8 | \([0, 0, 0, -45518403, -74365731902]\) | \(29689921233686449/10380965400750\) | \(3646812711557275610112000\) | \([2]\) | \(5308416\) | \(3.4144\) | |
35280.bj2 | 35280dy5 | \([0, 0, 0, -40649763, -99755096798]\) | \(21145699168383889/2593080\) | \(910943899822817280\) | \([2]\) | \(1769472\) | \(2.8651\) | |
35280.bj3 | 35280dy6 | \([0, 0, 0, -19058403, 31172624098]\) | \(2179252305146449/66177562500\) | \(23248047443394816000000\) | \([2, 2]\) | \(2654208\) | \(3.0679\) | |
35280.bj4 | 35280dy3 | \([0, 0, 0, -18917283, 31669112482]\) | \(2131200347946769/2058000\) | \(722971349065728000\) | \([2]\) | \(1327104\) | \(2.7213\) | |
35280.bj5 | 35280dy2 | \([0, 0, 0, -2547363, -1549971038]\) | \(5203798902289/57153600\) | \(20077947179768217600\) | \([2, 2]\) | \(884736\) | \(2.5186\) | |
35280.bj6 | 35280dy4 | \([0, 0, 0, -571683, -3892732382]\) | \(-58818484369/18600435000\) | \(-6534296202701352960000\) | \([2]\) | \(1769472\) | \(2.8651\) | |
35280.bj7 | 35280dy1 | \([0, 0, 0, -289443, 21089698]\) | \(7633736209/3870720\) | \(1359776316936683520\) | \([2]\) | \(442368\) | \(2.1720\) | \(\Gamma_0(N)\)-optimal |
35280.bj8 | 35280dy7 | \([0, 0, 0, 5143677, 104935723522]\) | \(42841933504271/13565917968750\) | \(-4765680279486000000000000\) | \([2]\) | \(5308416\) | \(3.4144\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.bj do not have complex multiplication.Modular form 35280.2.a.bj
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.