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SageMath
E = EllipticCurve("hs1")
E.isogeny_class()
Elliptic curves in class 141120.hs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.hs1 | 141120nr1 | \([0, 0, 0, -35868, -2616208]\) | \(-177953104/125\) | \(-3584673792000\) | \([]\) | \(414720\) | \(1.3453\) | \(\Gamma_0(N)\)-optimal |
141120.hs2 | 141120nr2 | \([0, 0, 0, 34692, -11111632]\) | \(161017136/1953125\) | \(-56010528000000000\) | \([]\) | \(1244160\) | \(1.8946\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.hs have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.hs do not have complex multiplication.Modular form 141120.2.a.hs
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.