Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 6930.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.m1 | 6930m3 | \([1, -1, 0, -296919, -62198825]\) | \(3971101377248209009/56495958750\) | \(41185553928750\) | \([2]\) | \(49152\) | \(1.7521\) | |
| 6930.m2 | 6930m2 | \([1, -1, 0, -19089, -909527]\) | \(1055257664218129/115307784900\) | \(84059375192100\) | \([2, 2]\) | \(24576\) | \(1.4055\) | |
| 6930.m3 | 6930m1 | \([1, -1, 0, -4509, 102325]\) | \(13908844989649/1980372240\) | \(1443691362960\) | \([2]\) | \(12288\) | \(1.0589\) | \(\Gamma_0(N)\)-optimal |
| 6930.m4 | 6930m4 | \([1, -1, 0, 25461, -4553717]\) | \(2503876820718671/13702874328990\) | \(-9989395385833710\) | \([2]\) | \(49152\) | \(1.7521\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.m have rank \(0\).
Complex multiplication
The elliptic curves in class 6930.m do not have complex multiplication.Modular form 6930.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
