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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 20160.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.bi1 | 20160dw3 | \([0, 0, 0, -802668, 171394288]\) | \(2394165105226952/854262178245\) | \(20406505568357744640\) | \([2]\) | \(491520\) | \(2.4061\) | |
| 20160.bi2 | 20160dw2 | \([0, 0, 0, -714468, 232393408]\) | \(13507798771700416/3544416225\) | \(10583570137190400\) | \([2, 2]\) | \(245760\) | \(2.0596\) | |
| 20160.bi3 | 20160dw1 | \([0, 0, 0, -714423, 232424152]\) | \(864335783029582144/59535\) | \(2777664960\) | \([2]\) | \(122880\) | \(1.7130\) | \(\Gamma_0(N)\)-optimal |
| 20160.bi4 | 20160dw4 | \([0, 0, 0, -626988, 291424912]\) | \(-1141100604753992/875529151875\) | \(-20914528312258560000\) | \([2]\) | \(491520\) | \(2.4061\) |
Rank
sage: E.rank()
The elliptic curves in class 20160.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 20160.bi do not have complex multiplication.Modular form 20160.2.a.bi
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.
