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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 302016i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302016.i2 | 302016i1 | \([0, -1, 0, -7905, 4715361]\) | \(-117649/20592\) | \(-9563008955056128\) | \([2]\) | \(3686400\) | \(1.7457\) | \(\Gamma_0(N)\)-optimal |
302016.i1 | 302016i2 | \([0, -1, 0, -472545, 124127841]\) | \(25128011089/245388\) | \(113959190047752192\) | \([2]\) | \(7372800\) | \(2.0923\) |
Rank
sage: E.rank()
The elliptic curves in class 302016i have rank \(0\).
Complex multiplication
The elliptic curves in class 302016i do not have complex multiplication.Modular form 302016.2.a.i
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.