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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 93600.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.ci1 | 93600v4 | \([0, 0, 0, -5765814300, 168515203808000]\) | \(454357982636417669333824/3003024375\) | \(140109105240000000000\) | \([2]\) | \(41287680\) | \(3.9247\) | |
93600.ci2 | 93600v3 | \([0, 0, 0, -385086675, 2251100825750]\) | \(1082883335268084577352/251301565117746585\) | \(1465590727766698083720000000\) | \([2]\) | \(41287680\) | \(3.9247\) | |
93600.ci3 | 93600v1 | \([0, 0, 0, -360370425, 2632942172000]\) | \(7099759044484031233216/577161945398025\) | \(420751058195160225000000\) | \([2, 2]\) | \(20643840\) | \(3.5782\) | \(\Gamma_0(N)\)-optimal |
93600.ci4 | 93600v2 | \([0, 0, 0, -335766675, 3007878718250]\) | \(-717825640026599866952/254764560814329735\) | \(-1485786918669171014520000000\) | \([2]\) | \(41287680\) | \(3.9247\) |
Rank
sage: E.rank()
The elliptic curves in class 93600.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 93600.ci do not have complex multiplication.Modular form 93600.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.