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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 74529.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74529.bc1 | 74529v3 | \([0, 0, 1, -8744736, -24531185156]\) | \(-178643795968/524596891\) | \(-217170881759983719303099\) | \([]\) | \(6967296\) | \(3.1648\) | |
| 74529.bc2 | 74529v1 | \([0, 0, 1, -546546, 155800804]\) | \(-43614208/91\) | \(-37671878311147899\) | \([]\) | \(774144\) | \(2.0662\) | \(\Gamma_0(N)\)-optimal |
| 74529.bc3 | 74529v2 | \([0, 0, 1, 944034, 772975453]\) | \(224755712/753571\) | \(-311960824294615751619\) | \([]\) | \(2322432\) | \(2.6155\) |
Rank
sage: E.rank()
The elliptic curves in class 74529.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 74529.bc do not have complex multiplication.Modular form 74529.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
