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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 124950.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 124950.bd1 | 124950i4 | \([1, 1, 0, -136282500, 611323404000]\) | \(152277495831664137649/282362258900400\) | \(519056834333955618750000\) | \([2]\) | \(28311552\) | \(3.4413\) | |
| 124950.bd2 | 124950i3 | \([1, 1, 0, -112174500, -454828200000]\) | \(84917632843343402929/537144431250000\) | \(987414143627050781250000\) | \([2]\) | \(28311552\) | \(3.4413\) | |
| 124950.bd3 | 124950i2 | \([1, 1, 0, -11332500, 2691954000]\) | \(87557366190249649/48960807840000\) | \(90002970024502500000000\) | \([2, 2]\) | \(14155776\) | \(3.0948\) | |
| 124950.bd4 | 124950i1 | \([1, 1, 0, 2779500, 335250000]\) | \(1291859362462031/773834342400\) | \(-1422513071078400000000\) | \([2]\) | \(7077888\) | \(2.7482\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 124950.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 124950.bd do not have complex multiplication.Modular form 124950.2.a.bd
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.
