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SageMath
E = EllipticCurve("hb1")
E.isogeny_class()
Elliptic curves in class 92400.hb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.hb1 | 92400if2 | \([0, 1, 0, -4488, 13428]\) | \(19530306557/11114334\) | \(5690539008000\) | \([2]\) | \(147456\) | \(1.1373\) | |
| 92400.hb2 | 92400if1 | \([0, 1, 0, 1112, 2228]\) | \(296740963/174636\) | \(-89413632000\) | \([2]\) | \(73728\) | \(0.79076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.hb have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.hb do not have complex multiplication.Modular form 92400.2.a.hb
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.
