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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 98736.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.bh1 | 98736bo2 | \([0, -1, 0, -31634850848, 2165703084052224]\) | \(362515826352179162139875/203046912\) | \(1961058293002568466432\) | \([2]\) | \(76640256\) | \(4.3139\) | |
| 98736.bh2 | 98736bo1 | \([0, -1, 0, -1977189408, 33839201357568]\) | \(88506348541062171875/2094601863168\) | \(20229986823459977400680448\) | \([2]\) | \(38320128\) | \(3.9673\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98736.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 98736.bh do not have complex multiplication.Modular form 98736.2.a.bh
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.
