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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 43120.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43120.bc1 | 43120cg2 | \([0, -1, 0, -62540, 8175532]\) | \(-18330740176/8857805\) | \(-13072251679182080\) | \([]\) | \(290304\) | \(1.7980\) | |
| 43120.bc2 | 43120cg1 | \([0, -1, 0, 6060, -138788]\) | \(16674224/15125\) | \(-22321309472000\) | \([]\) | \(96768\) | \(1.2487\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43120.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 43120.bc do not have complex multiplication.Modular form 43120.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
