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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 480.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480.f1 | 480d2 | \([0, 1, 0, -3601, -84385]\) | \(1261112198464/675\) | \(2764800\) | \([2]\) | \(384\) | \(0.56564\) | |
480.f2 | 480d3 | \([0, 1, 0, -496, 2204]\) | \(26410345352/10546875\) | \(5400000000\) | \([2]\) | \(384\) | \(0.56564\) | |
480.f3 | 480d1 | \([0, 1, 0, -226, -1360]\) | \(20034997696/455625\) | \(29160000\) | \([2, 2]\) | \(192\) | \(0.21907\) | \(\Gamma_0(N)\)-optimal |
480.f4 | 480d4 | \([0, 1, 0, 24, -3960]\) | \(2863288/13286025\) | \(-6802444800\) | \([4]\) | \(384\) | \(0.56564\) |
Rank
sage: E.rank()
The elliptic curves in class 480.f have rank \(0\).
Complex multiplication
The elliptic curves in class 480.f do not have complex multiplication.Modular form 480.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.