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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 31824h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31824.bk2 | 31824h1 | \([0, 0, 0, -498, 3175]\) | \(1171019776/304317\) | \(3549553488\) | \([2]\) | \(16384\) | \(0.54156\) | \(\Gamma_0(N)\)-optimal |
| 31824.bk1 | 31824h2 | \([0, 0, 0, -7383, 244150]\) | \(238481570896/25857\) | \(4825536768\) | \([2]\) | \(32768\) | \(0.88813\) |
Rank
sage: E.rank()
The elliptic curves in class 31824h have rank \(0\).
Complex multiplication
The elliptic curves in class 31824h do not have complex multiplication.Modular form 31824.2.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 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.
