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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 11310h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11310.h1 | 11310h1 | \([1, 1, 1, -9691, -123991]\) | \(100654290922421809/52033093632000\) | \(52033093632000\) | \([2]\) | \(38400\) | \(1.3240\) | \(\Gamma_0(N)\)-optimal |
11310.h2 | 11310h2 | \([1, 1, 1, 36389, -916567]\) | \(5328847957372469711/3458851344000000\) | \(-3458851344000000\) | \([2]\) | \(76800\) | \(1.6705\) |
Rank
sage: E.rank()
The elliptic curves in class 11310h have rank \(1\).
Complex multiplication
The elliptic curves in class 11310h do not have complex multiplication.Modular form 11310.2.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.