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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 397800.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.dd1 | 397800dd2 | \([0, 0, 0, -1864160653575, 979333283857630250]\) | \(245689277968779868090419995701456/93342399137270122585475925\) | \(272186435884279677459247797300000000\) | \([2]\) | \(5945425920\) | \(5.7656\) | |
| 397800.dd2 | 397800dd1 | \([0, 0, 0, -99358612950, 19963952147352125]\) | \(-595213448747095198927846967296/600281130562949295663181875\) | \(-109401236045097509134614896718750000\) | \([2]\) | \(2972712960\) | \(5.4190\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397800.dd have rank \(1\).
Complex multiplication
The elliptic curves in class 397800.dd do not have complex multiplication.Modular form 397800.2.a.dd
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.
