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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 13860.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13860.e1 | 13860l2 | \([0, 0, 0, -16383, -777418]\) | \(2605772594896/108945375\) | \(20331821664000\) | \([2]\) | \(27648\) | \(1.3185\) | |
13860.e2 | 13860l1 | \([0, 0, 0, 492, -45043]\) | \(1129201664/75796875\) | \(-884094750000\) | \([2]\) | \(13824\) | \(0.97190\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13860.e have rank \(0\).
Complex multiplication
The elliptic curves in class 13860.e do not have complex multiplication.Modular form 13860.2.a.e
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.