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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 234416.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 234416.h1 | 234416h2 | \([0, 1, 0, -3424773, 343096207]\) | \(147499655667712000/83658895553597\) | \(2519650663164194163968\) | \([]\) | \(8211456\) | \(2.7965\) | |
| 234416.h2 | 234416h1 | \([0, 1, 0, -2523173, 1541809471]\) | \(58984345526272000/187116293\) | \(5635595457320192\) | \([]\) | \(2737152\) | \(2.2472\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 234416.h have rank \(1\).
Complex multiplication
The elliptic curves in class 234416.h do not have complex multiplication.Modular form 234416.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
