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SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 310464fa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.fa4 | 310464fa1 | \([0, 0, 0, -18190956, -9879294544]\) | \(29609739866953/15259926528\) | \(343090057721035590991872\) | \([2]\) | \(35389440\) | \(3.2081\) | \(\Gamma_0(N)\)-optimal |
| 310464.fa2 | 310464fa2 | \([0, 0, 0, -162697836, 791671467440]\) | \(21184262604460873/216872764416\) | \(4875966416029522417680384\) | \([2, 2]\) | \(70778880\) | \(3.5547\) | |
| 310464.fa1 | 310464fa3 | \([0, 0, 0, -2596735596, 50931875708336]\) | \(86129359107301290313/9166294368\) | \(206086474796238511276032\) | \([2]\) | \(141557760\) | \(3.9013\) | |
| 310464.fa3 | 310464fa4 | \([0, 0, 0, -40770156, 1950715993520]\) | \(-333345918055753/72923718045024\) | \(-1639549350869575095262642176\) | \([2]\) | \(141557760\) | \(3.9013\) |
Rank
sage: E.rank()
The elliptic curves in class 310464fa have rank \(0\).
Complex multiplication
The elliptic curves in class 310464fa do not have complex multiplication.Modular form 310464.2.a.fa
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.
