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SageMath
E = EllipticCurve("hy1")
E.isogeny_class()
Elliptic curves in class 224400hy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.bd2 | 224400hy1 | \([0, -1, 0, -5339408, 4693671312]\) | \(1052163263816561956/14516937435825\) | \(232270998973200000000\) | \([2]\) | \(9289728\) | \(2.7136\) | \(\Gamma_0(N)\)-optimal |
224400.bd1 | 224400hy2 | \([0, -1, 0, -10252408, -5289544688]\) | \(3724357985033255138/1777091206460625\) | \(56866918606740000000000\) | \([2]\) | \(18579456\) | \(3.0602\) |
Rank
sage: E.rank()
The elliptic curves in class 224400hy have rank \(1\).
Complex multiplication
The elliptic curves in class 224400hy do not have complex multiplication.Modular form 224400.2.a.hy
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.