Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 4800.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4800.cj1 | 4800cl4 | \([0, 1, 0, -52993, -4697857]\) | \(502270291349/1889568\) | \(61917364224000\) | \([2]\) | \(15360\) | \(1.5057\) | |
4800.cj2 | 4800cl2 | \([0, 1, 0, -3393, 74943]\) | \(131872229/18\) | \(589824000\) | \([2]\) | \(3072\) | \(0.70102\) | |
4800.cj3 | 4800cl3 | \([0, 1, 0, -1793, -141057]\) | \(-19465109/248832\) | \(-8153726976000\) | \([2]\) | \(7680\) | \(1.1592\) | |
4800.cj4 | 4800cl1 | \([0, 1, 0, -193, 1343]\) | \(-24389/12\) | \(-393216000\) | \([2]\) | \(1536\) | \(0.35445\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4800.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 4800.cj do not have complex multiplication.Modular form 4800.2.a.cj
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.