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SageMath
E = EllipticCurve("hj1")
E.isogeny_class()
Elliptic curves in class 212160.hj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212160.hj1 | 212160ew1 | \([0, 1, 0, -69765, -7053525]\) | \(36672690756665344/371578664925\) | \(380496552883200\) | \([2]\) | \(1179648\) | \(1.6156\) | \(\Gamma_0(N)\)-optimal |
212160.hj2 | 212160ew2 | \([0, 1, 0, -17745, -17280657]\) | \(-37718660202064/7846581380625\) | \(-128558389340160000\) | \([2]\) | \(2359296\) | \(1.9622\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.hj have rank \(0\).
Complex multiplication
The elliptic curves in class 212160.hj do not have complex multiplication.Modular form 212160.2.a.hj
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.