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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 63426.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63426.bc1 | 63426bi4 | \([1, 0, 0, -335565844, -2366027948080]\) | \(4708545773991716929537/65472\) | \(58106641002432\) | \([2]\) | \(5898240\) | \(3.1273\) | |
| 63426.bc2 | 63426bi6 | \([1, 0, 0, -63141564, 148417258248]\) | \(31368919137792368257/7430386718185992\) | \(6594495563643577542636552\) | \([2]\) | \(11796480\) | \(3.4739\) | |
| 63426.bc3 | 63426bi3 | \([1, 0, 0, -21280404, -35830451376]\) | \(1200862149227882497/70094268661824\) | \(62208921454371744174144\) | \([2, 2]\) | \(5898240\) | \(3.1273\) | |
| 63426.bc4 | 63426bi2 | \([1, 0, 0, -20972884, -36970428016]\) | \(1149550394446181377/4286582784\) | \(3804357999711227904\) | \([2, 2]\) | \(2949120\) | \(2.7807\) | |
| 63426.bc5 | 63426bi1 | \([1, 0, 0, -1291604, -595486320]\) | \(-268498407453697/17163091968\) | \(-15232307298941534208\) | \([2]\) | \(1474560\) | \(2.4342\) | \(\Gamma_0(N)\)-optimal |
| 63426.bc6 | 63426bi5 | \([1, 0, 0, 15660436, -147118425960]\) | \(478591624936623743/10812469457036808\) | \(-9596106443820238452490248\) | \([2]\) | \(11796480\) | \(3.4739\) |
Rank
sage: E.rank()
The elliptic curves in class 63426.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 63426.bc do not have complex multiplication.Modular form 63426.2.a.bc
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
