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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 311696.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.cv1 | 311696cv2 | \([0, -1, 0, -2053168, 165781728]\) | \(263822189935250/149429406721\) | \(542153337241725913088\) | \([2]\) | \(11059200\) | \(2.6685\) | |
311696.cv2 | 311696cv1 | \([0, -1, 0, 507192, 20353280]\) | \(7953970437500/4703287687\) | \(-8532132902983072768\) | \([2]\) | \(5529600\) | \(2.3219\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 311696.cv have rank \(1\).
Complex multiplication
The elliptic curves in class 311696.cv do not have complex multiplication.Modular form 311696.2.a.cv
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.