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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 161700di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161700.bo2 | 161700di1 | \([0, -1, 0, -26133, -5090238]\) | \(-67108864/343035\) | \(-10089431178750000\) | \([2]\) | \(1105920\) | \(1.7552\) | \(\Gamma_0(N)\)-optimal |
| 161700.bo1 | 161700di2 | \([0, -1, 0, -632508, -193066488]\) | \(59466754384/121275\) | \(57071529900000000\) | \([2]\) | \(2211840\) | \(2.1017\) |
Rank
sage: E.rank()
The elliptic curves in class 161700di have rank \(0\).
Complex multiplication
The elliptic curves in class 161700di do not have complex multiplication.Modular form 161700.2.a.di
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.
