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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 5070h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5070.h1 | 5070h1 | \([1, 1, 0, -3795912, -2743222464]\) | \(570403428460237/23887872000\) | \(253318923646304256000\) | \([2]\) | \(336960\) | \(2.6799\) | \(\Gamma_0(N)\)-optimal |
5070.h2 | 5070h2 | \([1, 1, 0, 1828408, -10170699456]\) | \(63745936931123/4251528000000\) | \(-45085326010291944000000\) | \([2]\) | \(673920\) | \(3.0265\) |
Rank
sage: E.rank()
The elliptic curves in class 5070h have rank \(1\).
Complex multiplication
The elliptic curves in class 5070h do not have complex multiplication.Modular form 5070.2.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.