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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 17424.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.bi1 | 17424bm3 | \([0, 0, 0, -1402995, 637184306]\) | \(57736239625/255552\) | \(1351832463007285248\) | \([2]\) | \(276480\) | \(2.3313\) | |
| 17424.bi2 | 17424bm4 | \([0, 0, 0, -706035, 1270442162]\) | \(-7357983625/127552392\) | \(-674733378098511249408\) | \([2]\) | \(552960\) | \(2.6779\) | |
| 17424.bi3 | 17424bm1 | \([0, 0, 0, -96195, -10831678]\) | \(18609625/1188\) | \(6284345127616512\) | \([2]\) | \(92160\) | \(1.7820\) | \(\Gamma_0(N)\)-optimal |
| 17424.bi4 | 17424bm2 | \([0, 0, 0, 78045, -45714526]\) | \(9938375/176418\) | \(-933225251451052032\) | \([2]\) | \(184320\) | \(2.1286\) |
Rank
sage: E.rank()
The elliptic curves in class 17424.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 17424.bi do not have complex multiplication.Modular form 17424.2.a.bi
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
