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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 112710v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.bd2 | 112710v1 | \([1, 0, 1, -15179, -758794]\) | \(-16022066761/998400\) | \(-24098948889600\) | \([2]\) | \(394240\) | \(1.3219\) | \(\Gamma_0(N)\)-optimal |
112710.bd1 | 112710v2 | \([1, 0, 1, -246379, -47091274]\) | \(68523370149961/243360\) | \(5874118791840\) | \([2]\) | \(788480\) | \(1.6684\) |
Rank
sage: E.rank()
The elliptic curves in class 112710v have rank \(0\).
Complex multiplication
The elliptic curves in class 112710v do not have complex multiplication.Modular form 112710.2.a.v
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.