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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 57222h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57222.ba4 | 57222h1 | \([1, -1, 0, -5256, -1296]\) | \(912673/528\) | \(9290839958928\) | \([2]\) | \(163840\) | \(1.1778\) | \(\Gamma_0(N)\)-optimal |
| 57222.ba2 | 57222h2 | \([1, -1, 0, -57276, 5273532]\) | \(1180932193/4356\) | \(76649429661156\) | \([2, 2]\) | \(327680\) | \(1.5244\) | |
| 57222.ba3 | 57222h3 | \([1, -1, 0, -31266, 10064574]\) | \(-192100033/2371842\) | \(-41735614450499442\) | \([2]\) | \(655360\) | \(1.8710\) | |
| 57222.ba1 | 57222h4 | \([1, -1, 0, -915606, 337447242]\) | \(4824238966273/66\) | \(1161354994866\) | \([2]\) | \(655360\) | \(1.8710\) |
Rank
sage: E.rank()
The elliptic curves in class 57222h have rank \(0\).
Complex multiplication
The elliptic curves in class 57222h do not have complex multiplication.Modular form 57222.2.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.
