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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 152460h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.cc2 | 152460h1 | \([0, 0, 0, -23232, 4273841]\) | \(-67108864/343035\) | \(-7088299435934640\) | \([2]\) | \(921600\) | \(1.7257\) | \(\Gamma_0(N)\)-optimal |
| 152460.cc1 | 152460h2 | \([0, 0, 0, -562287, 162001334]\) | \(59466754384/121275\) | \(40095431152761600\) | \([2]\) | \(1843200\) | \(2.0723\) |
Rank
sage: E.rank()
The elliptic curves in class 152460h have rank \(0\).
Complex multiplication
The elliptic curves in class 152460h do not have complex multiplication.Modular form 152460.2.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.
