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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 37553.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37553.c1 | 37553a4 | \([1, -1, 1, -200329, 34561496]\) | \(82483294977/17\) | \(183246660593\) | \([2]\) | \(105984\) | \(1.5484\) | |
37553.c2 | 37553a2 | \([1, -1, 1, -12564, 538478]\) | \(20346417/289\) | \(3115193230081\) | \([2, 2]\) | \(52992\) | \(1.2019\) | |
37553.c3 | 37553a1 | \([1, -1, 1, -1519, -9354]\) | \(35937/17\) | \(183246660593\) | \([2]\) | \(26496\) | \(0.85529\) | \(\Gamma_0(N)\)-optimal |
37553.c4 | 37553a3 | \([1, -1, 1, -1519, 1444168]\) | \(-35937/83521\) | \(-900290843493409\) | \([2]\) | \(105984\) | \(1.5484\) |
Rank
sage: E.rank()
The elliptic curves in class 37553.c have rank \(1\).
Complex multiplication
The elliptic curves in class 37553.c do not have complex multiplication.Modular form 37553.2.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.