Show commands:
SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 2400.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2400.bh1 | 2400l3 | \([0, 1, 0, -90033, 10368063]\) | \(1261112198464/675\) | \(43200000000\) | \([2]\) | \(9216\) | \(1.3704\) | |
| 2400.bh2 | 2400l2 | \([0, 1, 0, -12408, -300312]\) | \(26410345352/10546875\) | \(84375000000000\) | \([2]\) | \(9216\) | \(1.3704\) | |
| 2400.bh3 | 2400l1 | \([0, 1, 0, -5658, 158688]\) | \(20034997696/455625\) | \(455625000000\) | \([2, 2]\) | \(4608\) | \(1.0238\) | \(\Gamma_0(N)\)-optimal |
| 2400.bh4 | 2400l4 | \([0, 1, 0, 592, 496188]\) | \(2863288/13286025\) | \(-106288200000000\) | \([2]\) | \(9216\) | \(1.3704\) |
Rank
sage: E.rank()
The elliptic curves in class 2400.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 2400.bh do not have complex multiplication.Modular form 2400.2.a.bh
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
