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SageMath
E = EllipticCurve("ht1")
E.isogeny_class()
Elliptic curves in class 381150.ht
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.ht1 | 381150ht1 | \([1, -1, 0, -135989442, -610327034784]\) | \(13782741913468081/701662500\) | \(14158978809350976562500\) | \([2]\) | \(66355200\) | \(3.3204\) | \(\Gamma_0(N)\)-optimal |
381150.ht2 | 381150ht2 | \([1, -1, 0, -128638692, -679240316034]\) | \(-11666347147400401/3126621093750\) | \(-63092671777779235839843750\) | \([2]\) | \(132710400\) | \(3.6670\) |
Rank
sage: E.rank()
The elliptic curves in class 381150.ht have rank \(0\).
Complex multiplication
The elliptic curves in class 381150.ht do not have complex multiplication.Modular form 381150.2.a.ht
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 LMFDB 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 LMFDB labels.