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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 12144.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12144.u1 | 12144ba2 | \([0, -1, 0, -477576, 93462768]\) | \(2940980566145956489/783792101714688\) | \(3210412448623362048\) | \([2]\) | \(368640\) | \(2.2595\) | |
| 12144.u2 | 12144ba1 | \([0, -1, 0, 75384, 9412848]\) | \(11566328890520951/16088147361792\) | \(-65897051593900032\) | \([2]\) | \(184320\) | \(1.9129\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12144.u have rank \(0\).
Complex multiplication
The elliptic curves in class 12144.u do not have complex multiplication.Modular form 12144.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
