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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 630.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
630.h1 | 630i7 | \([1, -1, 1, -3161093, 2164026557]\) | \(4791901410190533590281/41160000\) | \(30005640000\) | \([6]\) | \(9216\) | \(2.0516\) | |
630.h2 | 630i6 | \([1, -1, 1, -197573, 33848381]\) | \(1169975873419524361/108425318400\) | \(79042057113600\) | \([2, 6]\) | \(4608\) | \(1.7050\) | |
630.h3 | 630i8 | \([1, -1, 1, -183173, 38980541]\) | \(-932348627918877961/358766164249920\) | \(-261540533738191680\) | \([6]\) | \(9216\) | \(2.0516\) | |
630.h4 | 630i4 | \([1, -1, 1, -39218, 2946557]\) | \(9150443179640281/184570312500\) | \(134551757812500\) | \([2]\) | \(3072\) | \(1.5023\) | |
630.h5 | 630i3 | \([1, -1, 1, -13253, 449597]\) | \(353108405631241/86318776320\) | \(62926387937280\) | \([6]\) | \(2304\) | \(1.3584\) | |
630.h6 | 630i2 | \([1, -1, 1, -5198, -74419]\) | \(21302308926361/8930250000\) | \(6510152250000\) | \([2, 2]\) | \(1536\) | \(1.1557\) | |
630.h7 | 630i1 | \([1, -1, 1, -4478, -114163]\) | \(13619385906841/6048000\) | \(4408992000\) | \([2]\) | \(768\) | \(0.80912\) | \(\Gamma_0(N)\)-optimal |
630.h8 | 630i5 | \([1, -1, 1, 17302, -560419]\) | \(785793873833639/637994920500\) | \(-465098297044500\) | \([2]\) | \(3072\) | \(1.5023\) |
Rank
sage: E.rank()
The elliptic curves in class 630.h have rank \(0\).
Complex multiplication
The elliptic curves in class 630.h do not have complex multiplication.Modular form 630.2.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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.