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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 234234db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234234.db2 | 234234db1 | \([1, -1, 1, -616037, -290505315]\) | \(-7347774183121/6119866368\) | \(-21534241600553730048\) | \([2]\) | \(10321920\) | \(2.4075\) | \(\Gamma_0(N)\)-optimal |
234234.db1 | 234234db2 | \([1, -1, 1, -11323877, -14660426595]\) | \(45637459887836881/13417633152\) | \(47213212940986764672\) | \([2]\) | \(20643840\) | \(2.7541\) |
Rank
sage: E.rank()
The elliptic curves in class 234234db have rank \(1\).
Complex multiplication
The elliptic curves in class 234234db do not have complex multiplication.Modular form 234234.2.a.db
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.