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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 48841.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48841.c1 | 48841a4 | \([1, -1, 0, -4429268, -3586839541]\) | \(82483294977/17\) | \(1980626399884457\) | \([2]\) | \(663552\) | \(2.3224\) | |
| 48841.c2 | 48841a2 | \([1, -1, 0, -277783, -55586400]\) | \(20346417/289\) | \(33670648798035769\) | \([2, 2]\) | \(331776\) | \(1.9759\) | |
| 48841.c3 | 48841a3 | \([1, -1, 0, -33578, -150093735]\) | \(-35937/83521\) | \(-9730817502632337241\) | \([2]\) | \(663552\) | \(2.3224\) | |
| 48841.c4 | 48841a1 | \([1, -1, 0, -33578, 1020319]\) | \(35937/17\) | \(1980626399884457\) | \([2]\) | \(165888\) | \(1.6293\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48841.c have rank \(1\).
Complex multiplication
The elliptic curves in class 48841.c do not have complex multiplication.Modular form 48841.2.a.c
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.
