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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 5610c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.a2 | 5610c1 | \([1, 1, 0, -22788, -7267632]\) | \(-1308796492121439049/22000592486400000\) | \(-22000592486400000\) | \([2]\) | \(49920\) | \(1.8170\) | \(\Gamma_0(N)\)-optimal |
5610.a1 | 5610c2 | \([1, 1, 0, -719108, -234128688]\) | \(41125104693338423360329/179205840000000000\) | \(179205840000000000\) | \([2]\) | \(99840\) | \(2.1636\) |
Rank
sage: E.rank()
The elliptic curves in class 5610c have rank \(0\).
Complex multiplication
The elliptic curves in class 5610c do not have complex multiplication.Modular form 5610.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.