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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 91035.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91035.i1 | 91035l2 | \([1, -1, 1, -36698, 2715036]\) | \(1526038582697/2205\) | \(7897377285\) | \([2]\) | \(131072\) | \(1.1698\) | |
91035.i2 | 91035l1 | \([1, -1, 1, -2273, 43656]\) | \(-362467097/14175\) | \(-50768853975\) | \([2]\) | \(65536\) | \(0.82324\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.i have rank \(2\).
Complex multiplication
The elliptic curves in class 91035.i do not have complex multiplication.Modular form 91035.2.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 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.