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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 265200h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 265200.h4 | 265200h1 | \([0, -1, 0, -983, -31038]\) | \(-420616192/1456611\) | \(-364152750000\) | \([2]\) | \(393216\) | \(0.90445\) | \(\Gamma_0(N)\)-optimal |
| 265200.h3 | 265200h2 | \([0, -1, 0, -22108, -1256288]\) | \(298766385232/439569\) | \(1758276000000\) | \([2, 2]\) | \(786432\) | \(1.2510\) | |
| 265200.h2 | 265200h3 | \([0, -1, 0, -28608, -450288]\) | \(161838334948/87947613\) | \(1407161808000000\) | \([2]\) | \(1572864\) | \(1.5976\) | |
| 265200.h1 | 265200h4 | \([0, -1, 0, -353608, -80816288]\) | \(305612563186948/663\) | \(10608000000\) | \([2]\) | \(1572864\) | \(1.5976\) |
Rank
sage: E.rank()
The elliptic curves in class 265200h have rank \(1\).
Complex multiplication
The elliptic curves in class 265200h do not have complex multiplication.Modular form 265200.2.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 Cremona 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 Cremona labels.
