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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 6270k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6270.i2 | 6270k1 | \([1, 0, 1, 22476, 726322]\) | \(1255765531597770311/953441280000000\) | \(-953441280000000\) | \([2]\) | \(43008\) | \(1.5624\) | \(\Gamma_0(N)\)-optimal |
6270.i1 | 6270k2 | \([1, 0, 1, -104244, 6200626]\) | \(125276879181017571769/55842187500000000\) | \(55842187500000000\) | \([2]\) | \(86016\) | \(1.9090\) |
Rank
sage: E.rank()
The elliptic curves in class 6270k have rank \(0\).
Complex multiplication
The elliptic curves in class 6270k do not have complex multiplication.Modular form 6270.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.