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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 60984.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60984.h1 | 60984w2 | \([0, 0, 0, -253011, -48967490]\) | \(1354435492/539\) | \(712807664937984\) | \([2]\) | \(368640\) | \(1.8140\) | |
60984.h2 | 60984w1 | \([0, 0, 0, -13431, -1003574]\) | \(-810448/847\) | \(-280031582654208\) | \([2]\) | \(184320\) | \(1.4674\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60984.h have rank \(1\).
Complex multiplication
The elliptic curves in class 60984.h do not have complex multiplication.Modular form 60984.2.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.