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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 100016.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100016.h1 | 100016p4 | \([0, 0, 0, -97691, 7610314]\) | \(25172562615580017/8459034366482\) | \(34648204765110272\) | \([4]\) | \(454656\) | \(1.8761\) | |
| 100016.h2 | 100016p2 | \([0, 0, 0, -39931, -2982870]\) | \(1719073016770257/56424301444\) | \(231113938714624\) | \([2, 2]\) | \(227328\) | \(1.5295\) | |
| 100016.h3 | 100016p1 | \([0, 0, 0, -39611, -3034390]\) | \(1678074290715537/1900304\) | \(7783645184\) | \([2]\) | \(113664\) | \(1.1830\) | \(\Gamma_0(N)\)-optimal |
| 100016.h4 | 100016p3 | \([0, 0, 0, 12709, -10278774]\) | \(55424004754383/11175184480978\) | \(-45773555634085888\) | \([2]\) | \(454656\) | \(1.8761\) |
Rank
sage: E.rank()
The elliptic curves in class 100016.h have rank \(1\).
Complex multiplication
The elliptic curves in class 100016.h do not have complex multiplication.Modular form 100016.2.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.
