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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 159120.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.h1 | 159120bf3 | \([0, 0, 0, -9877683, 11945968882]\) | \(35694515311673154481/10400566692750\) | \(31055925735484416000\) | \([2]\) | \(6488064\) | \(2.7197\) | |
159120.h2 | 159120bf4 | \([0, 0, 0, -4834803, -3994692302]\) | \(4185743240664514801/113629394531250\) | \(339295554000000000000\) | \([2]\) | \(6488064\) | \(2.7197\) | |
159120.h3 | 159120bf2 | \([0, 0, 0, -697683, 134980882]\) | \(12577973014374481/4642947562500\) | \(13863767134464000000\) | \([2, 2]\) | \(3244032\) | \(2.3731\) | |
159120.h4 | 159120bf1 | \([0, 0, 0, 134637, 14960338]\) | \(90391899763439/84690294000\) | \(-252883862839296000\) | \([2]\) | \(1622016\) | \(2.0265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159120.h have rank \(1\).
Complex multiplication
The elliptic curves in class 159120.h do not have complex multiplication.Modular form 159120.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.