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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 273600v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.v4 | 273600v1 | \([0, 0, 0, -11775, 177500]\) | \(247673152/124659\) | \(90876411000000\) | \([2]\) | \(786432\) | \(1.3710\) | \(\Gamma_0(N)\)-optimal |
273600.v2 | 273600v2 | \([0, 0, 0, -102900, -12580000]\) | \(2582630848/29241\) | \(1364268096000000\) | \([2, 2]\) | \(1572864\) | \(1.7176\) | |
273600.v3 | 273600v3 | \([0, 0, 0, -21900, -31858000]\) | \(-3112136/1172889\) | \(-437778473472000000\) | \([2]\) | \(3145728\) | \(2.0642\) | |
273600.v1 | 273600v4 | \([0, 0, 0, -1641900, -809782000]\) | \(1311494070536/171\) | \(63825408000000\) | \([2]\) | \(3145728\) | \(2.0642\) |
Rank
sage: E.rank()
The elliptic curves in class 273600v have rank \(0\).
Complex multiplication
The elliptic curves in class 273600v do not have complex multiplication.Modular form 273600.2.a.v
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.