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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 180708.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180708.h1 | 180708j2 | \([0, -1, 0, -2064908, -1100646744]\) | \(1482435250000/60130587\) | \(39495330573970453248\) | \([2]\) | \(6303744\) | \(2.5262\) | |
180708.h2 | 180708j1 | \([0, -1, 0, -2044373, -1124409846]\) | \(23018340352000/40293\) | \(1654093027165392\) | \([2]\) | \(3151872\) | \(2.1796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 180708.h have rank \(0\).
Complex multiplication
The elliptic curves in class 180708.h do not have complex multiplication.Modular form 180708.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.