Show commands:
SageMath
E = EllipticCurve("bfe1")
E.isogeny_class()
Elliptic curves in class 705600.bfe
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.bfe1 | \([0, 0, 0, -88508700, 320486166000]\) | \(129348709488/6125\) | \(3630994498656000000000\) | \([2]\) | \(63700992\) | \(3.2109\) |
| 705600.bfe2 | \([0, 0, 0, -5821200, 4454541000]\) | \(588791808/109375\) | \(4052449217250000000000\) | \([2]\) | \(31850496\) | \(2.8643\) |
| 705600.bfe3 | \([0, 0, 0, -2072700, -460306000]\) | \(1210991472/588245\) | \(478354885666560000000\) | \([2]\) | \(21233664\) | \(2.6616\) |
| 705600.bfe4 | \([0, 0, 0, -1705200, -856471000]\) | \(10788913152/8575\) | \(435818955600000000\) | \([2]\) | \(10616832\) | \(2.3150\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bfe have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.bfe do not have complex multiplication.Modular form 705600.2.a.bfe
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.
