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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 6720.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.bv1 | 6720cc3 | \([0, 1, 0, -4481, -116961]\) | \(303735479048/105\) | \(3440640\) | \([2]\) | \(6144\) | \(0.61016\) | |
| 6720.bv2 | 6720cc2 | \([0, 1, 0, -281, -1881]\) | \(601211584/11025\) | \(45158400\) | \([2, 2]\) | \(3072\) | \(0.26359\) | |
| 6720.bv3 | 6720cc1 | \([0, 1, 0, -36, 30]\) | \(82881856/36015\) | \(2304960\) | \([2]\) | \(1536\) | \(-0.082988\) | \(\Gamma_0(N)\)-optimal |
| 6720.bv4 | 6720cc4 | \([0, 1, 0, -1, -5185]\) | \(-8/354375\) | \(-11612160000\) | \([2]\) | \(6144\) | \(0.61016\) |
Rank
sage: E.rank()
The elliptic curves in class 6720.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 6720.bv do not have complex multiplication.Modular form 6720.2.a.bv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
