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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 115920.fb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.fb1 | 115920ew4 | \([0, 0, 0, -727347, 238755634]\) | \(14251520160844849/264449745\) | \(789642707374080\) | \([2]\) | \(983040\) | \(1.9835\) | |
| 115920.fb2 | 115920ew2 | \([0, 0, 0, -46947, 3473314]\) | \(3832302404449/472410225\) | \(1410609373286400\) | \([2, 2]\) | \(491520\) | \(1.6369\) | |
| 115920.fb3 | 115920ew1 | \([0, 0, 0, -11667, -428654]\) | \(58818484369/7455105\) | \(22260824248320\) | \([2]\) | \(245760\) | \(1.2903\) | \(\Gamma_0(N)\)-optimal |
| 115920.fb4 | 115920ew3 | \([0, 0, 0, 68973, 17916946]\) | \(12152722588271/53476250625\) | \(-159679228746240000\) | \([2]\) | \(983040\) | \(1.9835\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.fb have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.fb do not have complex multiplication.Modular form 115920.2.a.fb
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 LMFDB 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 LMFDB labels.
