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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 5880.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5880.bf1 | 5880l4 | \([0, 1, 0, -183080, 30090528]\) | \(5633270409316/14175\) | \(1707698764800\) | \([4]\) | \(24576\) | \(1.5854\) | |
| 5880.bf2 | 5880l3 | \([0, 1, 0, -32160, -1635600]\) | \(30534944836/8203125\) | \(988251600000000\) | \([2]\) | \(24576\) | \(1.5854\) | |
| 5880.bf3 | 5880l2 | \([0, 1, 0, -11580, 455328]\) | \(5702413264/275625\) | \(8301313440000\) | \([2, 2]\) | \(12288\) | \(1.2389\) | |
| 5880.bf4 | 5880l1 | \([0, 1, 0, 425, 27950]\) | \(4499456/180075\) | \(-338970298800\) | \([2]\) | \(6144\) | \(0.89228\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5880.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 5880.bf do not have complex multiplication.Modular form 5880.2.a.bf
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
