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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 110466.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110466.l1 | 110466q3 | \([1, -1, 0, -2438442, -1107438476]\) | \(46753267515625/11591221248\) | \(397537708083519946752\) | \([2]\) | \(3981312\) | \(2.6630\) | |
110466.l2 | 110466q1 | \([1, -1, 0, -830187, 291246277]\) | \(1845026709625/793152\) | \(27202295728438848\) | \([2]\) | \(1327104\) | \(2.1136\) | \(\Gamma_0(N)\)-optimal |
110466.l3 | 110466q2 | \([1, -1, 0, -700227, 385415293]\) | \(-1107111813625/1228691592\) | \(-42139756370317830408\) | \([2]\) | \(2654208\) | \(2.4602\) | |
110466.l4 | 110466q4 | \([1, -1, 0, 5878998, -7027792268]\) | \(655215969476375/1001033261568\) | \(-34331884449861331026432\) | \([2]\) | \(7962624\) | \(3.0095\) |
Rank
sage: E.rank()
The elliptic curves in class 110466.l have rank \(0\).
Complex multiplication
The elliptic curves in class 110466.l do not have complex multiplication.Modular form 110466.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.