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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 14994.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14994.h1 | 14994bg4 | \([1, -1, 0, -2239848, 1290815784]\) | \(14489843500598257/6246072\) | \(535701366926712\) | \([2]\) | \(294912\) | \(2.1688\) | |
| 14994.h2 | 14994bg3 | \([1, -1, 0, -299448, -33263784]\) | \(34623662831857/14438442312\) | \(1238329190382511752\) | \([2]\) | \(294912\) | \(2.1688\) | |
| 14994.h3 | 14994bg2 | \([1, -1, 0, -140688, 19984320]\) | \(3590714269297/73410624\) | \(6296144460669504\) | \([2, 2]\) | \(147456\) | \(1.8222\) | |
| 14994.h4 | 14994bg1 | \([1, -1, 0, 432, 933120]\) | \(103823/4386816\) | \(-376240191860736\) | \([2]\) | \(73728\) | \(1.4757\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14994.h have rank \(0\).
Complex multiplication
The elliptic curves in class 14994.h do not have complex multiplication.Modular form 14994.2.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.
