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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 360640dz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360640.dz2 | 360640dz1 | \([0, 0, 0, -2791628, 2435184752]\) | \(-78013216986489/37918720000\) | \(-1169450464517816320000\) | \([2]\) | \(12386304\) | \(2.7481\) | \(\Gamma_0(N)\)-optimal |
360640.dz1 | 360640dz2 | \([0, 0, 0, -48953548, 131817814128]\) | \(420676324562824569/56350000000\) | \(1737889192345600000000\) | \([2]\) | \(24772608\) | \(3.0946\) |
Rank
sage: E.rank()
The elliptic curves in class 360640dz have rank \(0\).
Complex multiplication
The elliptic curves in class 360640dz do not have complex multiplication.Modular form 360640.2.a.dz
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.