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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 22800.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22800.h1 | 22800cl2 | \([0, -1, 0, -27208, 2812912]\) | \(-1392225385/1316928\) | \(-2107084800000000\) | \([]\) | \(103680\) | \(1.6367\) | |
22800.h2 | 22800cl1 | \([0, -1, 0, 2792, -67088]\) | \(1503815/2052\) | \(-3283200000000\) | \([]\) | \(34560\) | \(1.0874\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22800.h have rank \(1\).
Complex multiplication
The elliptic curves in class 22800.h do not have complex multiplication.Modular form 22800.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.