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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 91200gm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91200.o2 | 91200gm1 | \([0, -1, 0, 1867, 5637]\) | \(44957696/27075\) | \(-433200000000\) | \([2]\) | \(147456\) | \(0.92213\) | \(\Gamma_0(N)\)-optimal |
91200.o1 | 91200gm2 | \([0, -1, 0, -7633, 53137]\) | \(192143824/106875\) | \(27360000000000\) | \([2]\) | \(294912\) | \(1.2687\) |
Rank
sage: E.rank()
The elliptic curves in class 91200gm have rank \(1\).
Complex multiplication
The elliptic curves in class 91200gm do not have complex multiplication.Modular form 91200.2.a.gm
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.