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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 370881.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 370881.bb1 | 370881bb2 | \([1, -1, 0, -13174002, 18237048745]\) | \(4956477625/52983\) | \(2702964246181232939703\) | \([2]\) | \(20643840\) | \(2.9282\) | |
| 370881.bb2 | 370881bb1 | \([1, -1, 0, -193167, 710325328]\) | \(-15625/4263\) | \(-217479881876650926183\) | \([2]\) | \(10321920\) | \(2.5816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 370881.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 370881.bb do not have complex multiplication.Modular form 370881.2.a.bb
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.
