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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 234.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 234.d1 | 234b2 | \([1, -1, 1, -569, -5075]\) | \(1033364331/676\) | \(13305708\) | \([2]\) | \(96\) | \(0.30665\) | |
| 234.d2 | 234b1 | \([1, -1, 1, -29, -107]\) | \(-132651/208\) | \(-4094064\) | \([2]\) | \(48\) | \(-0.039925\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 234.d have rank \(0\).
Complex multiplication
The elliptic curves in class 234.d do not have complex multiplication.Modular form 234.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
