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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 91035u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91035.bl2 | 91035u1 | \([1, -1, 0, 2326019625, 178302165067336]\) | \(16098893047132187167/168182866341984375\) | \(-14539503308369857195506322359375\) | \([2]\) | \(137871360\) | \(4.6606\) | \(\Gamma_0(N)\)-optimal |
91035.bl1 | 91035u2 | \([1, -1, 0, -36838524870, 2527477705875325]\) | \(63953244990201015504593/5088175635498046875\) | \(439875643072107929613071044921875\) | \([2]\) | \(275742720\) | \(5.0072\) |
Rank
sage: E.rank()
The elliptic curves in class 91035u have rank \(1\).
Complex multiplication
The elliptic curves in class 91035u do not have complex multiplication.Modular form 91035.2.a.u
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.