Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 12480bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12480.cv3 | 12480bi1 | \([0, 1, 0, -865, 9215]\) | \(273359449/9360\) | \(2453667840\) | \([2]\) | \(6144\) | \(0.57361\) | \(\Gamma_0(N)\)-optimal |
| 12480.cv2 | 12480bi2 | \([0, 1, 0, -2145, -25857]\) | \(4165509529/1368900\) | \(358848921600\) | \([2, 2]\) | \(12288\) | \(0.92018\) | |
| 12480.cv1 | 12480bi3 | \([0, 1, 0, -30945, -2105217]\) | \(12501706118329/2570490\) | \(673838530560\) | \([2]\) | \(24576\) | \(1.2668\) | |
| 12480.cv4 | 12480bi4 | \([0, 1, 0, 6175, -170625]\) | \(99317171591/106616250\) | \(-27948810240000\) | \([4]\) | \(24576\) | \(1.2668\) |
Rank
sage: E.rank()
The elliptic curves in class 12480bi have rank \(0\).
Complex multiplication
The elliptic curves in class 12480bi do not have complex multiplication.Modular form 12480.2.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 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.
