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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 6930.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.l1 | 6930n3 | \([1, -1, 0, -871479, -312918147]\) | \(100407751863770656369/166028940000\) | \(121035097260000\) | \([2]\) | \(81920\) | \(1.9650\) | |
| 6930.l2 | 6930n2 | \([1, -1, 0, -54999, -4778595]\) | \(25238585142450289/995844326400\) | \(725970513945600\) | \([2, 2]\) | \(40960\) | \(1.6184\) | |
| 6930.l3 | 6930n1 | \([1, -1, 0, -8919, 225693]\) | \(107639597521009/32699842560\) | \(23838185226240\) | \([2]\) | \(20480\) | \(1.2719\) | \(\Gamma_0(N)\)-optimal |
| 6930.l4 | 6930n4 | \([1, -1, 0, 24201, -17466435]\) | \(2150235484224911/181905111732960\) | \(-132608826453327840\) | \([2]\) | \(81920\) | \(1.9650\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.l have rank \(0\).
Complex multiplication
The elliptic curves in class 6930.l do not have complex multiplication.Modular form 6930.2.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.
