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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7935k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7935.e4 | 7935k1 | \([1, 0, 0, 4750, 9507]\) | \(80062991/46575\) | \(-6894771530175\) | \([4]\) | \(21120\) | \(1.1529\) | \(\Gamma_0(N)\)-optimal |
7935.e3 | 7935k2 | \([1, 0, 0, -19055, 71400]\) | \(5168743489/2975625\) | \(440499292205625\) | \([2, 2]\) | \(42240\) | \(1.4995\) | |
7935.e2 | 7935k3 | \([1, 0, 0, -201560, -34714053]\) | \(6117442271569/26953125\) | \(3990029820703125\) | \([2]\) | \(84480\) | \(1.8461\) | |
7935.e1 | 7935k4 | \([1, 0, 0, -217430, 38913225]\) | \(7679186557489/20988075\) | \(3106988341023675\) | \([2]\) | \(84480\) | \(1.8461\) |
Rank
sage: E.rank()
The elliptic curves in class 7935k have rank \(0\).
Complex multiplication
The elliptic curves in class 7935k do not have complex multiplication.Modular form 7935.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.