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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 212940bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212940.e2 | 212940bx1 | \([0, 0, 0, -103428, 14590277]\) | \(-58680557568/10144225\) | \(-21152550180106800\) | \([2]\) | \(1290240\) | \(1.8587\) | \(\Gamma_0(N)\)-optimal |
| 212940.e1 | 212940bx2 | \([0, 0, 0, -1718223, 866879078]\) | \(16815061239408/398125\) | \(13282606078560000\) | \([2]\) | \(2580480\) | \(2.2053\) |
Rank
sage: E.rank()
The elliptic curves in class 212940bx have rank \(2\).
Complex multiplication
The elliptic curves in class 212940bx do not have complex multiplication.Modular form 212940.2.a.bx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
