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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 152880.el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152880.el1 | 152880bt2 | \([0, 1, 0, -3456463936, -78217251586636]\) | \(27629784261491295969847/311852531250\) | \(51545597902920576000000\) | \([2]\) | \(85155840\) | \(3.9262\) | |
152880.el2 | 152880bt1 | \([0, 1, 0, -215854816, -1224267626380]\) | \(-6729249553378150807/22664098606500\) | \(-3746112013008685651968000\) | \([2]\) | \(42577920\) | \(3.5796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152880.el have rank \(0\).
Complex multiplication
The elliptic curves in class 152880.el do not have complex multiplication.Modular form 152880.2.a.el
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.