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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 140790bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 140790.bq4 | 140790bm1 | \([1, 1, 1, -104156, -21418051]\) | \(-2656166199049/2658140160\) | \(-125054545648680960\) | \([2]\) | \(2211840\) | \(1.9763\) | \(\Gamma_0(N)\)-optimal |
| 140790.bq3 | 140790bm2 | \([1, 1, 1, -1952476, -1050562627]\) | \(17496824387403529/6580454400\) | \(309583274628326400\) | \([2, 2]\) | \(4423680\) | \(2.3229\) | |
| 140790.bq2 | 140790bm3 | \([1, 1, 1, -2241276, -719713347]\) | \(26465989780414729/10571870144160\) | \(497362944749604204960\) | \([2]\) | \(8847360\) | \(2.6695\) | |
| 140790.bq1 | 140790bm4 | \([1, 1, 1, -31236796, -67209698371]\) | \(71647584155243142409/10140000\) | \(477045233340000\) | \([2]\) | \(8847360\) | \(2.6695\) |
Rank
sage: E.rank()
The elliptic curves in class 140790bm have rank \(0\).
Complex multiplication
The elliptic curves in class 140790bm do not have complex multiplication.Modular form 140790.2.a.bm
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 Cremona 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 Cremona labels.
