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SageMath
E = EllipticCurve("iv1")
E.isogeny_class()
Elliptic curves in class 388080.iv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.iv1 | 388080iv3 | \([0, 0, 0, -455112, 9548091]\) | \(281370820608/161767375\) | \(5993637231500226000\) | \([2]\) | \(5971968\) | \(2.2927\) | |
| 388080.iv2 | 388080iv1 | \([0, 0, 0, -325752, 71561119]\) | \(75216478666752/326095\) | \(16573572282960\) | \([2]\) | \(1990656\) | \(1.7434\) | \(\Gamma_0(N)\)-optimal |
| 388080.iv3 | 388080iv2 | \([0, 0, 0, -320607, 73930906]\) | \(-4481782160112/310023175\) | \(-252107710955654400\) | \([2]\) | \(3981312\) | \(2.0900\) | |
| 388080.iv4 | 388080iv4 | \([0, 0, 0, 1813833, 76255074]\) | \(1113258734352/648484375\) | \(-384431542545204000000\) | \([2]\) | \(11943936\) | \(2.6393\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.iv have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.iv do not have complex multiplication.Modular form 388080.2.a.iv
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
