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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 64757.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64757.d1 | 64757h1 | \([0, -1, 1, -53263, 7147246]\) | \(-28094464000/20657483\) | \(-12287552641561043\) | \([]\) | \(282240\) | \(1.7867\) | \(\Gamma_0(N)\)-optimal |
| 64757.d2 | 64757h2 | \([0, -1, 1, 434517, -110188233]\) | \(15252992000000/17621717267\) | \(-10481808386479983707\) | \([]\) | \(846720\) | \(2.3360\) |
Rank
sage: E.rank()
The elliptic curves in class 64757.d have rank \(1\).
Complex multiplication
The elliptic curves in class 64757.d do not have complex multiplication.Modular form 64757.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
