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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 99666i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
99666.k2 | 99666i1 | \([1, -1, 0, -732510, 243149332]\) | \(-506814405937489/4048994304\) | \(-347266535405174784\) | \([]\) | \(1524096\) | \(2.1938\) | \(\Gamma_0(N)\)-optimal |
99666.k1 | 99666i2 | \([1, -1, 0, -3140370, -23770438448]\) | \(-39934705050538129/2823126576537804\) | \(-242128615561657058938284\) | \([]\) | \(10668672\) | \(3.1667\) |
Rank
sage: E.rank()
The elliptic curves in class 99666i have rank \(1\).
Complex multiplication
The elliptic curves in class 99666i do not have complex multiplication.Modular form 99666.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.