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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 77760.ed
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77760.ed1 | 77760db2 | \([0, 0, 0, -7452, -247536]\) | \(15768432/5\) | \(14511882240\) | \([]\) | \(62208\) | \(0.92508\) | |
77760.ed2 | 77760db1 | \([0, 0, 0, -252, 1104]\) | \(444528/125\) | \(497664000\) | \([]\) | \(20736\) | \(0.37578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77760.ed have rank \(1\).
Complex multiplication
The elliptic curves in class 77760.ed do not have complex multiplication.Modular form 77760.2.a.ed
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.