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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 23400i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23400.bi2 | 23400i1 | \([0, 0, 0, -75, -162250]\) | \(-4/975\) | \(-11372400000000\) | \([2]\) | \(36864\) | \(1.1841\) | \(\Gamma_0(N)\)-optimal |
| 23400.bi1 | 23400i2 | \([0, 0, 0, -45075, -3627250]\) | \(434163602/7605\) | \(177409440000000\) | \([2]\) | \(73728\) | \(1.5306\) |
Rank
sage: E.rank()
The elliptic curves in class 23400i have rank \(0\).
Complex multiplication
The elliptic curves in class 23400i do not have complex multiplication.Modular form 23400.2.a.i
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.
