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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 35520b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35520.m2 | 35520b1 | \([0, -1, 0, -9621, -373329]\) | \(-1539038632738816/66363694875\) | \(-4247276472000\) | \([]\) | \(60480\) | \(1.1889\) | \(\Gamma_0(N)\)-optimal |
| 35520.m1 | 35520b2 | \([0, -1, 0, -787221, -268577289]\) | \(-843013059301831868416/61543395\) | \(-3938777280\) | \([]\) | \(181440\) | \(1.7382\) |
Rank
sage: E.rank()
The elliptic curves in class 35520b have rank \(1\).
Complex multiplication
The elliptic curves in class 35520b do not have complex multiplication.Modular form 35520.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
