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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3822.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3822.h1 | 3822d3 | \([1, 1, 0, -95869, -11462975]\) | \(828279937799497/193444524\) | \(22758554804076\) | \([2]\) | \(18432\) | \(1.5536\) | |
3822.h2 | 3822d2 | \([1, 1, 0, -6689, -137115]\) | \(281397674377/96589584\) | \(11363667968016\) | \([2, 2]\) | \(9216\) | \(1.2070\) | |
3822.h3 | 3822d1 | \([1, 1, 0, -2769, 53397]\) | \(19968681097/628992\) | \(74000279808\) | \([2]\) | \(4608\) | \(0.86045\) | \(\Gamma_0(N)\)-optimal |
3822.h4 | 3822d4 | \([1, 1, 0, 19771, -925623]\) | \(7264187703863/7406095788\) | \(-871319763362412\) | \([2]\) | \(18432\) | \(1.5536\) |
Rank
sage: E.rank()
The elliptic curves in class 3822.h have rank \(0\).
Complex multiplication
The elliptic curves in class 3822.h do not have complex multiplication.Modular form 3822.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.