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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 224400el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.h1 | 224400el1 | \([0, -1, 0, -409710408, 3191682531312]\) | \(118843307222596927933249/19794099600000000\) | \(1266822374400000000000000\) | \([2]\) | \(77414400\) | \(3.6327\) | \(\Gamma_0(N)\)-optimal |
224400.h2 | 224400el2 | \([0, -1, 0, -369710408, 3839682531312]\) | \(-87323024620536113533249/48975797371840020000\) | \(-3134451031797761280000000000\) | \([2]\) | \(154828800\) | \(3.9793\) |
Rank
sage: E.rank()
The elliptic curves in class 224400el have rank \(1\).
Complex multiplication
The elliptic curves in class 224400el do not have complex multiplication.Modular form 224400.2.a.el
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.