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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 8112.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8112.bi1 | 8112bi2 | \([0, 1, 0, -3436, 66392]\) | \(3631696/507\) | \(626481193728\) | \([2]\) | \(16128\) | \(0.98995\) | |
| 8112.bi2 | 8112bi1 | \([0, 1, 0, -901, -9658]\) | \(1048576/117\) | \(9035786448\) | \([2]\) | \(8064\) | \(0.64337\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8112.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 8112.bi do not have complex multiplication.Modular form 8112.2.a.bi
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.
