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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 398502u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 398502.u4 | 398502u1 | \([1, -1, 0, -44901, -536171]\) | \(2845178713/1609728\) | \(5664220356907008\) | \([2]\) | \(2654208\) | \(1.7127\) | \(\Gamma_0(N)\)-optimal |
| 398502.u2 | 398502u2 | \([1, -1, 0, -531621, -148791083]\) | \(4722184089433/9884736\) | \(34781853129132096\) | \([2, 2]\) | \(5308416\) | \(2.0593\) | |
| 398502.u3 | 398502u3 | \([1, -1, 0, -349101, -252644963]\) | \(-1337180541913/7067998104\) | \(-24870474231209829144\) | \([2]\) | \(10616832\) | \(2.4059\) | |
| 398502.u1 | 398502u4 | \([1, -1, 0, -8501661, -9539092211]\) | \(19312898130234073/84888\) | \(298699120383768\) | \([2]\) | \(10616832\) | \(2.4059\) |
Rank
sage: E.rank()
The elliptic curves in class 398502u have rank \(0\).
Complex multiplication
The elliptic curves in class 398502u do not have complex multiplication.Modular form 398502.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
