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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 102960h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.k1 | 102960h1 | \([0, 0, 0, -378, 1107]\) | \(18966528/9295\) | \(2927255760\) | \([2]\) | \(55296\) | \(0.50973\) | \(\Gamma_0(N)\)-optimal |
102960.k2 | 102960h2 | \([0, 0, 0, 1377, 8478]\) | \(57305232/39325\) | \(-198152697600\) | \([2]\) | \(110592\) | \(0.85630\) |
Rank
sage: E.rank()
The elliptic curves in class 102960h have rank \(1\).
Complex multiplication
The elliptic curves in class 102960h do not have complex multiplication.Modular form 102960.2.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.