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SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 221760hi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221760.j1 | 221760hi1 | \([0, 0, 0, -485028, 130016448]\) | \(156521104308288/13475\) | \(1086375628800\) | \([2]\) | \(1376256\) | \(1.7503\) | \(\Gamma_0(N)\)-optimal |
221760.j2 | 221760hi2 | \([0, 0, 0, -483948, 130624272]\) | \(-19434733194456/181575625\) | \(-117111292784640000\) | \([2]\) | \(2752512\) | \(2.0969\) |
Rank
sage: E.rank()
The elliptic curves in class 221760hi have rank \(2\).
Complex multiplication
The elliptic curves in class 221760hi do not have complex multiplication.Modular form 221760.2.a.hi
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.