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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 97020.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.f1 | 97020bk4 | \([0, 0, 0, -110248383, -445560267418]\) | \(6749703004355978704/5671875\) | \(124532407692000000\) | \([2]\) | \(4976640\) | \(3.0158\) | |
97020.f2 | 97020bk3 | \([0, 0, 0, -6889008, -6965095543]\) | \(-26348629355659264/24169921875\) | \(-33167367105468750000\) | \([2]\) | \(2488320\) | \(2.6692\) | |
97020.f3 | 97020bk2 | \([0, 0, 0, -1391943, -582034642]\) | \(13584145739344/1195803675\) | \(26255217326667436800\) | \([2]\) | \(1658880\) | \(2.4665\) | |
97020.f4 | 97020bk1 | \([0, 0, 0, 96432, -42349867]\) | \(72268906496/606436875\) | \(-832187814401790000\) | \([2]\) | \(829440\) | \(2.1199\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.f have rank \(0\).
Complex multiplication
The elliptic curves in class 97020.f do not have complex multiplication.Modular form 97020.2.a.f
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.