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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 40460b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40460.d2 | 40460b1 | \([0, -1, 0, -1541, -113759]\) | \(-65536/875\) | \(-5406815456000\) | \([]\) | \(60480\) | \(1.1248\) | \(\Gamma_0(N)\)-optimal |
| 40460.d1 | 40460b2 | \([0, -1, 0, -232741, -43140079]\) | \(-225637236736/1715\) | \(-10597358293760\) | \([]\) | \(181440\) | \(1.6742\) |
Rank
sage: E.rank()
The elliptic curves in class 40460b have rank \(0\).
Complex multiplication
The elliptic curves in class 40460b do not have complex multiplication.Modular form 40460.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
