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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 493680.hh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.hh1 | 493680hh2 | \([0, 1, 0, -359520080, -2623932536172]\) | \(708234550511150304361/23696640000\) | \(171950257172643840000\) | \([2]\) | \(81100800\) | \(3.3824\) | |
493680.hh2 | 493680hh1 | \([0, 1, 0, -22501200, -40885032300]\) | \(173629978755828841/1000026931200\) | \(7256509277239718707200\) | \([2]\) | \(40550400\) | \(3.0358\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 493680.hh have rank \(0\).
Complex multiplication
The elliptic curves in class 493680.hh do not have complex multiplication.Modular form 493680.2.a.hh
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.