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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 101478h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101478.l2 | 101478h1 | \([1, 0, 0, 12, -624]\) | \(190109375/168859392\) | \(-168859392\) | \([2]\) | \(40896\) | \(0.25773\) | \(\Gamma_0(N)\)-optimal |
101478.l1 | 101478h2 | \([1, 0, 0, -1028, -12480]\) | \(120151572738625/3168549072\) | \(3168549072\) | \([2]\) | \(81792\) | \(0.60431\) |
Rank
sage: E.rank()
The elliptic curves in class 101478h have rank \(0\).
Complex multiplication
The elliptic curves in class 101478h do not have complex multiplication.Modular form 101478.2.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.