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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 3806.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3806.i1 | 3806k2 | \([1, 1, 1, -234707185, -1383324033177]\) | \(1429890781632517784976214749841/931085992986663052734184\) | \(931085992986663052734184\) | \([]\) | \(950400\) | \(3.5391\) | |
3806.i2 | 3806k1 | \([1, 1, 1, -8886825, 10184752663]\) | \(77618205794496589164982801/74344901644570230784\) | \(74344901644570230784\) | \([5]\) | \(190080\) | \(2.7344\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3806.i have rank \(0\).
Complex multiplication
The elliptic curves in class 3806.i do not have complex multiplication.Modular form 3806.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.