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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 405600fh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405600.fh3 | 405600fh1 | \([0, 1, 0, -6766955758, 214241224047488]\) | \(7099759044484031233216/577161945398025\) | \(2785850472504695652225000000\) | \([2, 2]\) | \(433520640\) | \(4.3113\) | \(\Gamma_0(N)\)-optimal* |
405600.fh1 | 405600fh2 | \([0, 1, 0, -108269179633, 13712108457168863]\) | \(454357982636417669333824/3003024375\) | \(927681605150040000000000\) | \([2]\) | \(867041280\) | \(4.6579\) | \(\Gamma_0(N)\)-optimal* |
405600.fh4 | 405600fh3 | \([0, 1, 0, -6304952008, 244750103682488]\) | \(-717825640026599866952/254764560814329735\) | \(-9837599000157232750924920000000\) | \([2]\) | \(867041280\) | \(4.6579\) | |
405600.fh2 | 405600fh4 | \([0, 1, 0, -7231072008, 183170497574988]\) | \(1082883335268084577352/251301565117746585\) | \(9703877249795402209578120000000\) | \([2]\) | \(867041280\) | \(4.6579\) |
Rank
sage: E.rank()
The elliptic curves in class 405600fh have rank \(0\).
Complex multiplication
The elliptic curves in class 405600fh do not have complex multiplication.Modular form 405600.2.a.fh
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.