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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 161700.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161700.bl1 | 161700dc2 | \([0, -1, 0, -473748, 125664792]\) | \(3123406998416/17787\) | \(66963928416000\) | \([2]\) | \(1695744\) | \(1.8442\) | |
| 161700.bl2 | 161700dc1 | \([0, -1, 0, -29073, 2045142]\) | \(-11550212096/922383\) | \(-217034875134000\) | \([2]\) | \(847872\) | \(1.4976\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161700.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 161700.bl do not have complex multiplication.Modular form 161700.2.a.bl
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 LMFDB 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 LMFDB labels.
