Show commands:
SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 100800.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.dg1 | 100800h4 | \([0, 0, 0, -380700, -36234000]\) | \(1210991472/588245\) | \(2964077141760000000\) | \([2]\) | \(1327104\) | \(2.2379\) | |
| 100800.dg2 | 100800h3 | \([0, 0, 0, -313200, -67419000]\) | \(10788913152/8575\) | \(2700507600000000\) | \([2]\) | \(663552\) | \(1.8913\) | |
| 100800.dg3 | 100800h2 | \([0, 0, 0, -200700, 34606000]\) | \(129348709488/6125\) | \(42336000000000\) | \([2]\) | \(442368\) | \(1.6886\) | |
| 100800.dg4 | 100800h1 | \([0, 0, 0, -13200, 481000]\) | \(588791808/109375\) | \(47250000000000\) | \([2]\) | \(221184\) | \(1.3420\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 100800.dg do not have complex multiplication.Modular form 100800.2.a.dg
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.
