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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1470h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1470.g3 | 1470h1 | \([1, 0, 1, -173, 536]\) | \(4826809/1680\) | \(197650320\) | \([2]\) | \(768\) | \(0.29339\) | \(\Gamma_0(N)\)-optimal |
| 1470.g2 | 1470h2 | \([1, 0, 1, -1153, -14752]\) | \(1439069689/44100\) | \(5188320900\) | \([2, 2]\) | \(1536\) | \(0.63997\) | |
| 1470.g1 | 1470h3 | \([1, 0, 1, -18303, -954572]\) | \(5763259856089/5670\) | \(667069830\) | \([2]\) | \(3072\) | \(0.98654\) | |
| 1470.g4 | 1470h4 | \([1, 0, 1, 317, -49444]\) | \(30080231/9003750\) | \(-1059282183750\) | \([2]\) | \(3072\) | \(0.98654\) |
Rank
sage: E.rank()
The elliptic curves in class 1470h have rank \(0\).
Complex multiplication
The elliptic curves in class 1470h do not have complex multiplication.Modular form 1470.2.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.
