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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 3520m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3520.k1 | 3520m1 | \([0, -1, 0, -65, 577]\) | \(-117649/440\) | \(-115343360\) | \([]\) | \(768\) | \(0.23262\) | \(\Gamma_0(N)\)-optimal |
3520.k2 | 3520m2 | \([0, -1, 0, 575, -13375]\) | \(80062991/332750\) | \(-87228416000\) | \([]\) | \(2304\) | \(0.78192\) |
Rank
sage: E.rank()
The elliptic curves in class 3520m have rank \(1\).
Complex multiplication
The elliptic curves in class 3520m do not have complex multiplication.Modular form 3520.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.