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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 28798v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28798.bb2 | 28798v1 | \([1, 1, 1, 3809, 19141]\) | \(3449795831/2071552\) | \(-3669880732672\) | \([2]\) | \(102400\) | \(1.1002\) | \(\Gamma_0(N)\)-optimal |
28798.bb1 | 28798v2 | \([1, 1, 1, -15551, 135301]\) | \(234770924809/130960928\) | \(232005272568608\) | \([2]\) | \(204800\) | \(1.4468\) |
Rank
sage: E.rank()
The elliptic curves in class 28798v have rank \(0\).
Complex multiplication
The elliptic curves in class 28798v do not have complex multiplication.Modular form 28798.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.