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SageMath
E = EllipticCurve("byq1")
E.isogeny_class()
Elliptic curves in class 6350400.byq
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
6350400.byq1 | \([0, 0, 0, -793800, -270884250]\) | \(884736/5\) | \(312617511045000000\) | \([]\) | \(89579520\) | \(2.1989\) |
6350400.byq2 | \([0, 0, 0, -58800, 5230750]\) | \(2359296/125\) | \(1191196125000000\) | \([]\) | \(29859840\) | \(1.6496\) |
Rank
sage: E.rank()
The elliptic curves in class 6350400.byq have rank \(1\).
Complex multiplication
The elliptic curves in class 6350400.byq do not have complex multiplication.Modular form 6350400.2.a.byq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.