Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 11830l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11830.h4 | 11830l1 | \([1, -1, 0, 391, -4835]\) | \(1367631/2800\) | \(-13515065200\) | \([2]\) | \(7680\) | \(0.62831\) | \(\Gamma_0(N)\)-optimal |
| 11830.h3 | 11830l2 | \([1, -1, 0, -2989, -50127]\) | \(611960049/122500\) | \(591284102500\) | \([2, 2]\) | \(15360\) | \(0.97489\) | |
| 11830.h1 | 11830l3 | \([1, -1, 0, -45239, -3692077]\) | \(2121328796049/120050\) | \(579458420450\) | \([2]\) | \(30720\) | \(1.3215\) | |
| 11830.h2 | 11830l4 | \([1, -1, 0, -14819, 652575]\) | \(74565301329/5468750\) | \(26396611718750\) | \([2]\) | \(30720\) | \(1.3215\) |
Rank
sage: E.rank()
The elliptic curves in class 11830l have rank \(1\).
Complex multiplication
The elliptic curves in class 11830l do not have complex multiplication.Modular form 11830.2.a.l
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.
