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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 237160.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
237160.e1 | 237160e2 | \([0, 1, 0, -1424936, 465154864]\) | \(2185454/625\) | \(91505761754274560000\) | \([2]\) | \(6881280\) | \(2.5368\) | |
237160.e2 | 237160e1 | \([0, 1, 0, 235184, 48132720]\) | \(19652/25\) | \(-1830115235085491200\) | \([2]\) | \(3440640\) | \(2.1902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 237160.e have rank \(1\).
Complex multiplication
The elliptic curves in class 237160.e do not have complex multiplication.Modular form 237160.2.a.e
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.