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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 202800.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.h1 | 202800ep4 | \([0, -1, 0, -1401991608, -20204874054288]\) | \(986551739719628473/111045168\) | \(34303604243770368000000\) | \([2]\) | \(82575360\) | \(3.7484\) | |
| 202800.h2 | 202800ep3 | \([0, -1, 0, -158151608, 259690169712]\) | \(1416134368422073/725251155408\) | \(224041523467758916608000000\) | \([2]\) | \(82575360\) | \(3.7484\) | |
| 202800.h3 | 202800ep2 | \([0, -1, 0, -87847608, -313990470288]\) | \(242702053576633/2554695936\) | \(789185877513486336000000\) | \([2, 2]\) | \(41287680\) | \(3.4018\) | |
| 202800.h4 | 202800ep1 | \([0, -1, 0, -1319608, -12180806288]\) | \(-822656953/207028224\) | \(-63954284470861824000000\) | \([2]\) | \(20643840\) | \(3.0553\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.h have rank \(0\).
Complex multiplication
The elliptic curves in class 202800.h do not have complex multiplication.Modular form 202800.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
