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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 161700bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161700.eu2 | 161700bj1 | \([0, 1, 0, -12133, 423863]\) | \(1007878144/179685\) | \(35218260000000\) | \([]\) | \(373248\) | \(1.3187\) | \(\Gamma_0(N)\)-optimal |
| 161700.eu1 | 161700bj2 | \([0, 1, 0, -936133, 348309863]\) | \(462893166690304/4125\) | \(808500000000\) | \([]\) | \(1119744\) | \(1.8680\) |
Rank
sage: E.rank()
The elliptic curves in class 161700bj have rank \(1\).
Complex multiplication
The elliptic curves in class 161700bj do not have complex multiplication.Modular form 161700.2.a.bj
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.
