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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 930a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 930.b3 | 930a1 | \([1, 1, 0, -108, -432]\) | \(141339344329/17141760\) | \(17141760\) | \([2]\) | \(288\) | \(0.11858\) | \(\Gamma_0(N)\)-optimal |
| 930.b2 | 930a2 | \([1, 1, 0, -428, 2832]\) | \(8702409880009/1120910400\) | \(1120910400\) | \([2, 2]\) | \(576\) | \(0.46515\) | |
| 930.b1 | 930a3 | \([1, 1, 0, -6628, 204952]\) | \(32208729120020809/658986840\) | \(658986840\) | \([2]\) | \(1152\) | \(0.81173\) | |
| 930.b4 | 930a4 | \([1, 1, 0, 652, 16008]\) | \(30579142915511/124675335000\) | \(-124675335000\) | \([2]\) | \(1152\) | \(0.81173\) |
Rank
sage: E.rank()
The elliptic curves in class 930a have rank \(1\).
Complex multiplication
The elliptic curves in class 930a do not have complex multiplication.Modular form 930.2.a.a
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.
