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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 4830.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4830.ba1 | 4830ba4 | \([1, 0, 0, -432781, 109548761]\) | \(8964546681033941529169/31696875000\) | \(31696875000\) | \([2]\) | \(36864\) | \(1.6573\) | |
| 4830.ba2 | 4830ba3 | \([1, 0, 0, -36061, 471785]\) | \(5186062692284555089/2903809817953800\) | \(2903809817953800\) | \([2]\) | \(36864\) | \(1.6573\) | |
| 4830.ba3 | 4830ba2 | \([1, 0, 0, -27061, 1708385]\) | \(2191574502231419089/4115217960000\) | \(4115217960000\) | \([2, 2]\) | \(18432\) | \(1.3107\) | |
| 4830.ba4 | 4830ba1 | \([1, 0, 0, -1141, 44321]\) | \(-164287467238609/757170892800\) | \(-757170892800\) | \([4]\) | \(9216\) | \(0.96413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4830.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 4830.ba do not have complex multiplication.Modular form 4830.2.a.ba
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.
