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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 63525.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63525.bd1 | 63525d2 | \([0, -1, 1, -1020433, -396407232]\) | \(35084566528/1029\) | \(3446488883578125\) | \([]\) | \(684288\) | \(2.0812\) | |
| 63525.bd2 | 63525d1 | \([0, -1, 1, -22183, 397143]\) | \(360448/189\) | \(633028570453125\) | \([]\) | \(228096\) | \(1.5318\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63525.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 63525.bd do not have complex multiplication.Modular form 63525.2.a.bd
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
