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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 70560i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70560.h1 | 70560i1 | \([0, 0, 0, -384993, 91943208]\) | \(42581671488/875\) | \(129678374952000\) | \([2]\) | \(552960\) | \(1.8273\) | \(\Gamma_0(N)\)-optimal |
70560.h2 | 70560i2 | \([0, 0, 0, -371763, 98555562]\) | \(-4792616856/765625\) | \(-907748624664000000\) | \([2]\) | \(1105920\) | \(2.1739\) |
Rank
sage: E.rank()
The elliptic curves in class 70560i have rank \(0\).
Complex multiplication
The elliptic curves in class 70560i do not have complex multiplication.Modular form 70560.2.a.i
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.