Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 117600.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117600.l1 | 117600ba4 | \([0, -1, 0, -39608, 3046212]\) | \(7301384/3\) | \(2823576000000\) | \([2]\) | \(294912\) | \(1.3515\) | |
| 117600.l2 | 117600ba3 | \([0, -1, 0, -21233, -1161663]\) | \(140608/3\) | \(22588608000000\) | \([2]\) | \(294912\) | \(1.3515\) | |
| 117600.l3 | 117600ba1 | \([0, -1, 0, -2858, 32712]\) | \(21952/9\) | \(1058841000000\) | \([2, 2]\) | \(147456\) | \(1.0049\) | \(\Gamma_0(N)\)-optimal |
| 117600.l4 | 117600ba2 | \([0, -1, 0, 9392, 228712]\) | \(97336/81\) | \(-76236552000000\) | \([2]\) | \(294912\) | \(1.3515\) |
Rank
sage: E.rank()
The elliptic curves in class 117600.l have rank \(2\).
Complex multiplication
The elliptic curves in class 117600.l do not have complex multiplication.Modular form 117600.2.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 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.
