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SageMath
E = EllipticCurve("hn1")
E.isogeny_class()
Elliptic curves in class 473200.hn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
473200.hn1 | 473200hn2 | \([0, -1, 0, -415458, 103326287]\) | \(-262885120/343\) | \(-10347471793750000\) | \([]\) | \(4665600\) | \(1.9800\) | \(\Gamma_0(N)\)-optimal* |
473200.hn2 | 473200hn1 | \([0, -1, 0, 7042, 658787]\) | \(1280/7\) | \(-211172893750000\) | \([]\) | \(1555200\) | \(1.4307\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 473200.hn have rank \(0\).
Complex multiplication
The elliptic curves in class 473200.hn do not have complex multiplication.Modular form 473200.2.a.hn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.