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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 94640.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.v1 | 94640ce3 | \([0, -1, 0, -136560646096, 20599625350185920]\) | \(-14245586655234650511684983641/1028175397808386133196800\) | \(-20327654456197523305224245293875200\) | \([]\) | \(768144384\) | \(5.3328\) | |
| 94640.v2 | 94640ce1 | \([0, -1, 0, -1564122096, -25817003132480]\) | \(-21405018343206000779641/2177246093750000000\) | \(-43045482662000000000000000000\) | \([]\) | \(85349376\) | \(4.2342\) | \(\Gamma_0(N)\)-optimal |
| 94640.v3 | 94640ce2 | \([0, -1, 0, 9632127904, 23677857867520]\) | \(4998853083179567995470359/2905108466204672000000\) | \(-57435765516914305645150208000000\) | \([]\) | \(256048128\) | \(4.7835\) |
Rank
sage: E.rank()
The elliptic curves in class 94640.v have rank \(1\).
Complex multiplication
The elliptic curves in class 94640.v do not have complex multiplication.Modular form 94640.2.a.v
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
