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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 705600.v
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.v1 | \([0, 0, 0, -434700, -108486000]\) | \(1314036/25\) | \(172832486400000000\) | \([2]\) | \(9437184\) | \(2.1010\) |
705600.v2 | \([0, 0, 0, -56700, 2646000]\) | \(11664/5\) | \(8641624320000000\) | \([2]\) | \(4718592\) | \(1.7544\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.v have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.v do not have complex multiplication.Modular form 705600.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.