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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 46800.fp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.fp1 | 46800dp2 | \([0, 0, 0, -1631595, -802170470]\) | \(-6434774386429585/140608\) | \(-10496330956800\) | \([]\) | \(622080\) | \(2.0248\) | |
46800.fp2 | 46800dp1 | \([0, 0, 0, -18795, -1253990]\) | \(-9836106385/3407872\) | \(-254396281651200\) | \([]\) | \(207360\) | \(1.4755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.fp have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.fp do not have complex multiplication.Modular form 46800.2.a.fp
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.