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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1323.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1323.h1 | 1323n2 | \([0, 0, 1, -20874, -1160798]\) | \(35184082944/7\) | \(200120949\) | \([]\) | \(1728\) | \(0.98228\) | |
| 1323.h2 | 1323n3 | \([0, 0, 1, -10584, 419060]\) | \(56623104/7\) | \(16209796869\) | \([]\) | \(1728\) | \(0.98228\) | |
| 1323.h3 | 1323n1 | \([0, 0, 1, -294, -1115]\) | \(884736/343\) | \(1089547389\) | \([]\) | \(576\) | \(0.43298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1323.h have rank \(1\).
Complex multiplication
The elliptic curves in class 1323.h do not have complex multiplication.Modular form 1323.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
