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SageMath
E = EllipticCurve("jz1")
E.isogeny_class()
Elliptic curves in class 277200jz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.jz3 | 277200jz1 | \([0, 0, 0, -732675, 241213250]\) | \(932288503609/779625\) | \(36374184000000000\) | \([2]\) | \(3538944\) | \(2.1056\) | \(\Gamma_0(N)\)-optimal |
277200.jz2 | 277200jz2 | \([0, 0, 0, -894675, 126679250]\) | \(1697509118089/833765625\) | \(38900169000000000000\) | \([2, 2]\) | \(7077888\) | \(2.4522\) | |
277200.jz4 | 277200jz3 | \([0, 0, 0, 3263325, 970753250]\) | \(82375335041831/56396484375\) | \(-2631234375000000000000\) | \([2]\) | \(14155776\) | \(2.7988\) | |
277200.jz1 | 277200jz4 | \([0, 0, 0, -7644675, -8047570750]\) | \(1058993490188089/13182390375\) | \(615037605336000000000\) | \([2]\) | \(14155776\) | \(2.7988\) |
Rank
sage: E.rank()
The elliptic curves in class 277200jz have rank \(0\).
Complex multiplication
The elliptic curves in class 277200jz do not have complex multiplication.Modular form 277200.2.a.jz
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.