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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 44400bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44400.k2 | 44400bv1 | \([0, -1, 0, -126208, -17209088]\) | \(27790593389/11988\) | \(95904000000000\) | \([2]\) | \(153600\) | \(1.6428\) | \(\Gamma_0(N)\)-optimal |
| 44400.k1 | 44400bv2 | \([0, -1, 0, -146208, -11369088]\) | \(43206601229/17964018\) | \(143712144000000000\) | \([2]\) | \(307200\) | \(1.9894\) |
Rank
sage: E.rank()
The elliptic curves in class 44400bv have rank \(1\).
Complex multiplication
The elliptic curves in class 44400bv do not have complex multiplication.Modular form 44400.2.a.bv
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.
