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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 361998b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361998.b2 | 361998b1 | \([1, -1, 0, 20034, -10263564]\) | \(7217724376967/373190157536\) | \(-45977400598592736\) | \([]\) | \(4665600\) | \(1.8770\) | \(\Gamma_0(N)\)-optimal |
| 361998.b1 | 361998b2 | \([1, -1, 0, -180621, 279763173]\) | \(-5289511417479913/271292372320256\) | \(-33423491562227859456\) | \([]\) | \(13996800\) | \(2.4263\) |
Rank
sage: E.rank()
The elliptic curves in class 361998b have rank \(1\).
Complex multiplication
The elliptic curves in class 361998b do not have complex multiplication.Modular form 361998.2.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.
