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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 101400k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101400.bs4 | 101400k1 | \([0, -1, 0, -9697783, -9796740188]\) | \(83587439220736/13990184325\) | \(16881986902892231250000\) | \([2]\) | \(6193152\) | \(2.9861\) | \(\Gamma_0(N)\)-optimal |
| 101400.bs2 | 101400k2 | \([0, -1, 0, -148298908, -695040702188]\) | \(18681746265374416/693005625\) | \(13380023151202500000000\) | \([2, 2]\) | \(12386304\) | \(3.3327\) | |
| 101400.bs3 | 101400k3 | \([0, -1, 0, -141454408, -762103113188]\) | \(-4053153720264484/903687890625\) | \(-69790861498556250000000000\) | \([2]\) | \(24772608\) | \(3.6793\) | |
| 101400.bs1 | 101400k4 | \([0, -1, 0, -2372761408, -44485809477188]\) | \(19129597231400697604/26325\) | \(2033051950800000000\) | \([2]\) | \(24772608\) | \(3.6793\) |
Rank
sage: E.rank()
The elliptic curves in class 101400k have rank \(1\).
Complex multiplication
The elliptic curves in class 101400k do not have complex multiplication.Modular form 101400.2.a.k
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 Cremona 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 Cremona labels.
