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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 4680.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4680.l1 | 4680q3 | \([0, 0, 0, -5054403, 4373739502]\) | \(19129597231400697604/26325\) | \(19651507200\) | \([2]\) | \(49152\) | \(2.1414\) | |
| 4680.l2 | 4680q2 | \([0, 0, 0, -315903, 68338402]\) | \(18681746265374416/693005625\) | \(129331481760000\) | \([2, 2]\) | \(24576\) | \(1.7948\) | |
| 4680.l3 | 4680q4 | \([0, 0, 0, -301323, 74931478]\) | \(-4053153720264484/903687890625\) | \(-674599395600000000\) | \([2]\) | \(49152\) | \(2.1414\) | |
| 4680.l4 | 4680q1 | \([0, 0, 0, -20658, 963493]\) | \(83587439220736/13990184325\) | \(163181509966800\) | \([2]\) | \(12288\) | \(1.4483\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4680.l have rank \(0\).
Complex multiplication
The elliptic curves in class 4680.l do not have complex multiplication.Modular form 4680.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
