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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 110670.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110670.h1 | 110670h2 | \([1, 1, 0, -71493, -7373547]\) | \(40413249107617335769/89198633968920\) | \(89198633968920\) | \([2]\) | \(497664\) | \(1.5597\) | |
110670.h2 | 110670h1 | \([1, 1, 0, -2893, -197987]\) | \(-2679190243489369/15177850430400\) | \(-15177850430400\) | \([2]\) | \(248832\) | \(1.2132\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 110670.h have rank \(1\).
Complex multiplication
The elliptic curves in class 110670.h do not have complex multiplication.Modular form 110670.2.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.