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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 372810.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 372810.bs1 | 372810bs3 | \([1, 0, 1, -18676630353, 982382752002256]\) | \(29848722870958822727928595369/1151947402954101562500\) | \(27805209923175430297851562500\) | \([2]\) | \(634060800\) | \(4.5428\) | |
| 372810.bs2 | 372810bs4 | \([1, 0, 1, -5611599273, -148767558476672]\) | \(809636604063811579913301289/72440506789459032037500\) | \(1748537731025535858478366837500\) | \([2]\) | \(634060800\) | \(4.5428\) | |
| 372810.bs3 | 372810bs2 | \([1, 0, 1, -1222411773, 13820236248328]\) | \(8369177043498476846301289/1424836952675156250000\) | \(34392100258946318570156250000\) | \([2, 2]\) | \(317030400\) | \(4.1963\) | |
| 372810.bs4 | 372810bs1 | \([1, 0, 1, 142801107, 1226966558056]\) | \(13342122094697556567191/34664215800981600000\) | \(-836709900727083637730400000\) | \([2]\) | \(158515200\) | \(3.8497\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 372810.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 372810.bs do not have complex multiplication.Modular form 372810.2.a.bs
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.
