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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 388080d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.d2 | 388080d1 | \([0, 0, 0, -819675003, 11358334230698]\) | \(-59465789423385795028207/20003531867239219200\) | \(-20487467551979786417366630400\) | \([2]\) | \(294174720\) | \(4.1444\) | \(\Gamma_0(N)\)-optimal |
| 388080.d1 | 388080d2 | \([0, 0, 0, -14031732603, 639715866452138]\) | \(298315634894429753085191407/22212303505611816960\) | \(22749674924718972909146603520\) | \([2]\) | \(588349440\) | \(4.4910\) |
Rank
sage: E.rank()
The elliptic curves in class 388080d have rank \(0\).
Complex multiplication
The elliptic curves in class 388080d do not have complex multiplication.Modular form 388080.2.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 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.
